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DOI: 10.1036/0071425586
When I was young, people called me a gambler. As the
scale of my operations increased I became known as a
speculator. Now I am called a banker. But I have been
doing the same thing all the time.
—Sir Ernest Cassell
Banker to Edward VII
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To my parents with love and gratitude
The suggestion that I write a book about risk came from the late Fischer
Black, while I was working at Goldman Sachs. The vastness of the project
is daunting. The topic touches on the most profound depths of statistics,
mathematics, psychology, and economics. I would like to thank the editors
and reviewers and those who provided comments, especially M.R. Carey
and Jean Eske, who carefully read the entire manuscript and provided
valuable comments, corrections, and advice.
I end with a note of thanks to my family, my friends, and my faculty
colleagues at Sloan, who inspired much of the enthusiasm that went into
the creation of this book and endured me with patience.
Cambridge, Massachusetts
February 2003
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For more information about this title, click here.
Chapter 1
Risk Management: A Maturing Discipline 1
Background 1
Risks: A View of the Past Decades 5
Definition of Risk 7
Related Terms and Differentiation 8
Degree of Risk 10
Risk Management: A Multilayered Term 11
1.6.1 Background 11
1.6.2 History of Modern Risk Management 11
1.6.3 Related Approaches 13
1.6.4 Approach and Risk Maps 22
1.7 Systemic Risk 22
1.7.1 Definition 22
1.7.2 Causes of Systemic Risk 26
1.7.3 Factors That Support Systemic Risk 26
1.7.4 Regulatory Mechanisms for Risk Management 27
1.8 Summary 28
1.9 Notes 30
Chapter 2
Market Risk 33
Background 33
Definition of Market Risk 34
Conceptual Approaches for Modeling Market Risk 37
Modern Portfolio Theory 39
2.4.1 The Capital Asset Pricing Model 41
2.4.2 The Security Market Line 43
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2.4.3 Modified Form of CAPM by Black, Jensen, and Scholes 45
2.4.4 Arbitrage Pricing Theory 46
2.4.5 Approaches to Option Pricing 47
Regulatory Initiatives for Market Risks and Value at Risk 54
2.5.1 Development of an International Framework
for Risk Regulation 56
2.5.2 Framework of the 1988 BIS Capital Adequacy Calculation 56
2.5.3 Criticisms of the 1988 Approach 58
2.5.4 Evolution of the 1996 Amendment on Market Risks 58
Amendment to the Capital Accord to Incorporate
Market Risks 60
2.6.1 Scope and Coverage of Capital Charges 60
2.6.2 Countable Capital Components 61
2.6.3 The de Minimis Rule 62
The Standardized Measurement Method 62
2.7.1 General and Specific Risks for Equity- and
Interest-Rate-Sensitive Instruments 65
2.7.2 Interest-Rate Risks 66
2.7.3 Equity Position Risk 79
2.7.4 Foreign-Exchange Risk 83
2.7.5 Commodities Risk 84
2.7.6 Treatment of Options 88
2.7.7 Criticisms of the Standard Approach 94
The Internal Model Approach 95
2.8.1 Conditions for and Process of Granting Approval 95
2.8.2 VaR-Based Components and Multiplication Factor 97
2.8.3 Requirement for Specific Risks 98
2.8.4 Combination of Model-Based and Standard Approaches 98
2.8.5 Specification of Market Risk Factors to Be Captured 99
2.8.6 Minimum Quantitative Requirements 101
2.8.7 Minimum Qualitative Requirements 102
The Precommitment Model 107
Comparison of Approaches 108
Revision and Modification of the Basel Accord
on Market Risks 109
2.11.1 The E.U. Capital Adequacy Directive 109
2.11.2 New Capital Adequacy Framework to Replace
the 1988 Accord 110
2.12 Regulation of Nonbanks 110
2.12.1 Pension Funds 111
2.12.2 Insurance Companies 111
2.12.3 Securities Firms 112
2.12.4 The Trend Toward Risk-Based Disclosures 113
2.12.5 Disclosure Requirements 113
2.12.6 Encouraged Disclosures 114
2.13 Market Instruments and Credit Risks 114
2.14 Summary 116
2.15 Notes 117
Chapter 3
Credit Risk 129
Background 129
Definition 130
Current Credit Risk Regulations 130
Deficiencies of the Current Regulations 131
Deficiencies of the Current Conceptual Approaches
for Modeling Credit Risk 133
3.6 Conceptual Approaches for Modeling Credit Risk 135
3.6.1 Transaction and Portfolio Management 136
3.6.2 Measuring Transaction Risk–Adjusted Profitability 140
3.7 Measuring Credit Risk for Credit Portfolios 140
3.7.1 Economic Capital Allocation 141
3.7.2 Choice of Time Horizon 146
3.7.3 Credit Loss Measurement Definition 146
3.7.4 Risk Aggregation 149
3.8 Development of New Approaches to Credit
Risk Management 150
3.8.1 Background 151
3.8.2 BIS Risk-Based Capital Requirement Framework 152
3.8.3 Traditional Credit Risk Management Approaches 154
3.8.4 Option Theory, Credit Risk, and the KMV Model 159
3.8.5 J. P. Morgan’s CreditMetrics and Other VaR
Approaches 167
3.8.6 The McKinsey Model and Other
Macrosimulation Models 178
3.8.7 KPMG’s Loan Analysis System and Other Risk-Neutral
Valuation Approaches 183
3.8.8 The CSFB CreditRisk+ Model 190
3.8.9 CSFB’s CreditRisk+ Approach 193
3.8.10 Summary and Comparison of New Internal
Model Approaches 197
Modern Portfolio Theory and Its Application
to Loan Portfolios 205
3.9.1 Background 205
3.9.2 Application to Nontraded Bonds and Credits 208
3.9.3 Nonnormal Returns 209
3.9.4 Unobservable Returns 209
3.9.5 Unobservable Correlations 209
3.9.6 Modeling Risk–Return Trade-off of Loans
and Loan Portfolios 209
3.9.7 Differences in Credit Versus Market Risk Models 225
Backtesting and Stress Testing Credit Risk Models 226
3.10.1 Background 226
3.10.2 Credit Risk Models and Backtesting 227
3.10.3 Stress Testing Based on Time-Series Versus
Cross-Sectional Approaches 228
Products with Inherent Credit Risks 229
3.11.1 Credit Lines 229
3.11.2 Secured Loans 231
3.11.3 Money Market Instruments 233
3.11.4 Futures Contracts 237
3.11.5 Options 240
3.11.6 Forward Rate Agreements 243
3.11.7 Asset-Backed Securities 245
3.11.8 Interest-Rate Swaps 247
Proposal for a Modern Capital Accord
for Credit Risk 250
3.12.1 Institute of International Finance 251
3.12.2 International Swaps and Derivatives Association 252
3.12.3 Basel Committee on Banking Supervision
and the New Capital Accord 253
Summary 263
Notes 265
Chapter 4
Operational Risk 283
4.1 Background 283
4.2 Increasing Focus on Operational Risk 285
4.2.1 Drivers of Operational Risk Management 286
4.2.2 Operational Risk and Shareholder Value 288
4.3 Definition of Operational Risk 289
4.4 Regulatory Understanding of Operational Risk Definition 293
4.5 Enforcement of Operational Risk Management 296
4.6 Evolution of Operational Risk Initiatives 299
4.7 Measurement of Operational Risk 302
4.8 Core Elements of an Operational Risk Management Process 303
4.9 Alternative Operational Risk Management Approaches 304
4.9.1 Top-Down Approaches 305
4.9.2 Bottom-Up Approaches 314
4.9.3 Top-Down vs. Bottom-Up Approaches 319
4.9.4 The Emerging Operational Risk Discussion 321
4.10 Capital Issues from the Regulatory Perspective 321
4.11 Capital Adequacy Issues from an Industry Perspective 324
4.11.1 Measurement Techniques and Progress
in the Industry Today 327
4.11.2 Regulatory Framework for Operational Risk Overview
Under the New Capital Accord 330
4.11.3 Operational Risk Standards 335
4.11.4 Possible Role of Bank Supervisors 336
4.12 Summary and Conclusion 337
4.13 Notes 338
Chapter 5
Building Blocks for Integration of Risk Categories 341
5.1 Background 341
5.2 The New Basel Capital Accord 342
5.2.1 Background 342
5.2.2 Existing Framework 343
5.2.3 Impact of the 1988 Accord 345
5.2.4 The June 1999 Proposal 346
5.2.5 Potential Modifications to the Committee’s Proposals 348
5.3 Structure of the New Accord and Impact
on Risk Management 352
5.3.1 Pillar I: Minimum Capital Requirement 352
5.3.2 Pillar II: Supervisory Review Process 353
5.3.3 Pillar III: Market Discipline and General
Disclosure Requirements 354
5.4 Value at Risk and Regulatory Capital Requirement 356
5.4.1 Background 356
5.4.2 Historical Development of VaR 357
5.4.3 VaR and Modern Financial Management 359
5.4.4 Definition of VaR 364
5.5 Conceptual Overview of Risk Methodologies 366
5.6 Limitations of VaR 368
5.6.1 Parameters for VaR Analysis 368
5.6.2 Different Approaches to Measuring VaR 373
5.6.3 Historical Simulation Method 380
5.6.4 Stress Testing 382
5.6.5 Summary of Stress Tests 389
5.7 Portfolio Risk 389
5.7.1 Portfolio VaR 390
5.7.2 Incremental VaR 393
5.7.3 Alternative Covariance Matrix Approaches 395
5.8 Pitfalls in the Application and Interpretation of VaR 404
5.8.1 Event and Stability Risks 405
5.8.2 Transition Risk 406
5.8.3 Changing Holdings 406
5.8.4 Problem Positions 406
5.8.5 Model Risks 407
5.8.6 Strategic Risks 409
5.8.7 Time Aggregation 409
5.8.8 Predicting Volatility and Correlations 414
5.8.9 Modeling Time-Varying Risk 415
5.8.10 The RiskMetrics Approach 423
5.8.11 Modeling Correlations 427
5.9 Liquidity Risk 431
5.10 Summary 436
5.11 Notes 437
Chapter 6
Case Studies 441
6.1 Structure of Studies 441
6.2 Overview of Cases 441
6.3 Metallgesellschaft 445
6.3.1 Background 445
6.3.2 Cause 448
6.3.3 Risk Areas Affected
6.4 Sumitomo 461
6.4.1 Background 461
6.4.2 Cause 461
6.4.3 Effect 464
6.4.4 Risk Areas Affected
6.5 LTCM 466
6.5.1 Background 466
6.5.2 Cause 468
6.5.3 Effect 472
6.5.4 Risk Areas Affected
6.6 Barings 479
6.6.1 Background 479
6.6.2 Cause 480
6.6.3 Effect 485
6.6.4 Risk Areas Affected
6.7 Notes 490
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Over the past decades, investors, regulators, and industry self-regulatory
bodies have forced banks, other financial institutions, and insurance companies to develop organizational structures and processes for the management of credit, market, and operational risk. Risk management became a hot
topic for many institutions, as a means of increasing shareholder value and
demonstrating the willingness and capability of top management to handle
this issue. In most financial organizations, risk management is mainly understood as the job area of the chief risk officer and is limited, for the most
part, to market risks. The credit risk officer usually takes care of credit risk
issues. Both areas are supervised at the board level by separate competence
and reporting lines and separate directives. More and more instruments,
strategies, and structured services have combined the profile characteristics
of credit and market risk, but most management concepts treat the different
parts of risk management separately. Only a few institutions have started to
develop an overall risk management approach, with the aim of quantifying
the overall risk exposures of the company (Figure I-1).
This book presents an inventory of the different approaches to market,
credit and, operational risk. The following chapters provide an in-depth
analysis of how the different risk areas diverge regarding methodologies,
assumptions, and conditions. The book also discusses how the different approaches can be identified and measured, and how their various parts contribute to the discipline of risk management as a whole. The closing chapter
provides case studies showing the relevance of the different risk categories
and discusses the “crash-testing” of regulatory rules through their application to various crises and accidents.
The objective of this book is to demonstrate the extent to which these
risk areas can be combined from a management standpoint, and to which
some of the methodologies and approaches are or are not reasonable for
economic, regulatory, or other purposes.
Most institutions treat market, credit, operational, and systemic risk as
separate management issues, which are therefore managed through separate competence directives and reporting lines. With the increased complexity and speed of events, regulators have implemented more and more
regulations regarding how to measure, report, and disclose risk managexvii
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F I G U R E I-1
Interaction and Integration of Risk Categories.
Increasing volatility
Market risk
1 2 3 4
Increasing operational risks
Operational risk
Credit risk
ment issues. As a result, one problem is to understand how the different
risk categories are defined, and what characteristics, assumptions, and
conditions are connected to the terms used to describe them. This allows
us to understand the different natures of different types of risk. And because risk has to be measured, measurement tools, methodologies, and so
forth must also be examined.
To this end, a scheme has been developed which allows a systematic
screening of the different issues characterizing the natures of the different
risk areas. It also helps determine the extent to which different risks can be
combined. Many methodologies that claim to provide “total enterprise
risk management,” “enterprisewide risk management,” and the like do
not prove whether the underlying risks share enough similarities, or the
risk areas share close enough assumptions, to justify considering them as
a homogeneous whole.
This scheme is applied to case studies, to examine the extent to
which some organizational structures, processes, models, assumptions,
methodologies, and so forth have proved applicable, and the extent of the
serious financial, reputational, and sometimes existential damages that
have resulted when they have not.
This work focuses on the level above the financial instruments and is intended to add value at the organization, transaction, and process levels so
as to increase the store of knowledge already accumulated. The pricing of
instruments and the valuation of portfolios are not the primary objects of
this book. Substantial knowledge has already been developed in this area
and is in continuous development. Risk management at the instrument
level is an essential basis for understanding how to make an institution’s
risk management structures, processes, and organizations efficient and
This book aims to develop a scheme or structure to screen and compare the different risk areas. This scheme must be structured in such a
way that it considers the appropriateness and usefulness of the different
methodologies, assumptions, and conditions for economic and regulatory
The objectives of this book are as follows:
Define the main terms used for the setup of the scheme, such as
systemic, market, credit, and operational risk.
Review the methodologies, assumptions, and conditions
connected to these terms.
Structure the characteristics of the different risk areas in such a
way that the screening of these risk areas allows comparison of
the different risk areas for economic and regulatory purposes.
In a subsequent step, this scheme is applied to a selection of case
studies. These are mainly publicized banking failures from the past decade
or so. The structured analysis of these relevant case studies should demonstrate the major causes and effects of each loss and the extent to which risk
control measures were or were not appropriate and effective.
The objectives of the case study analyses are as follows:
Highlight past loss experiences.
Detail previous losses in terms of systemic, market, credit, and
operational risks.
Highlight the impact of the losses.
Provide practical assistance in the development of improved risk
management through knowledge transfer and management
Generate future risk management indicators to mitigate the
potential likelihood of such disasters.
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Risk Management:
A Maturing Discipline
he entire history of human society is a chronology of exposure to risks
of all kinds and human efforts to deal with those risks. From the first
emergence of the species Homo sapiens, our ancestors practiced risk management in order to survive, not only as individuals but as a species. The
survival instinct drove humans to avoid the risks that threatened extinction and strive for security. Our actual physical existence is proof of our
ancestors’ success in applying risk management strategies.
Originally, our ancestors faced the same risks as other animals: the
hazardous environment, weather, starvation, and the threat of being
hunted by predators that were stronger and faster than humans. The environment was one of continuous peril, with chronic hunger and danger,
and we can only speculate how hard it must have been to achieve a semblance of security in such a threatening world.
In response to risk, our early ancestors learned to avoid dangerous
areas and situations. However, their instinctive reactions to risk and their
adaptive behavior do not adequately answer our questions about how they
successfully managed the different risks they faced. Other hominids did not
attain the ultimate goal of survival—including H. sapiens neanderthalensis,
despite the fact that they were larger and stronger than modern humans.
The modern humans, H. sapiens sapiens, not only survived all their relatives
but proved more resilient and excelled in adaptation and risk management.
Figure 1-1 shows the threats that humans have been exposed to over
the ages, and which probably will continue in the next century, as well. It
is obvious that these threats have shifted from the individual to society
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F I G U R E 1-1
Development of the Threats to Individuals, Groups, Nations, and the World.
Environmental destruction
Exhaustion of nonrenewable energy
Atomic threat
Wars on national level
Economic underdevelopment
Threats to social security
Lack of work
Life at subsistence level
Local wars
Diseases, epidemics
Robbery, tyranny
Slavery, violations of human rights
Stone Age
Middle Ages
Risk Management: A Maturing Discipline
and the global community. Thousands of years ago, humans first learned
to cultivate the wild herbs, grasses, grains, and roots that they had traditionally gathered. Concurrently, humans were creating the first settlements and domesticating wild animals. Next, humans began to grow,
harvest, and stockpile grain, which helped to form the concept of ownership. Over time, humans learned to defend their possessions and their interests, to accumulate foodstuffs and other goods for the future, and to
live together in tribal and other communal settings. As wealth accumulated in modest increments, rules about how to live together were needed,
and the first laws to govern human interaction were developed. Thus, the
beginning of civilization was launched. Walled cities, fortifications, and
other measures to protect property and communities demonstrate that
with increases in wealth came increased risk in a new form. Old forms,
which had threatened humans for generations, were replaced by new
threats. Famine and pestilence were frequent crises, and the perils of nature destroyed what communities and individuals had built. Warfare and
plundering increased the threats. As a result, our ancestors created technologies, war strategies, and social and legal rules to survive.
The evolution of business risks coincides with the start of trading and
commerce. We do not know exactly when trading and commerce began,
but their rise is clearly connected with the fact that society took advantage
of specialization, which increased the capacity to produce and stockpile
goods for future use. Stockpiling goods acts as a cushion against misfortune, the perils of nature, and the ravages of war. It is very probable that
business, in the form of trading and commerce, was one of the first active
efforts of society to deal with risk. Artifacts unearthed by archaeologists
prove that those early businesspeople developed techniques for dealing
with risk. Two major techniques are noteworthy and should be mentioned.
First, in 3000 B.C., the Babylonian civilization, with its extensive trade
relations, exhibited a highly developed bureaucracy and trading sector
with a monetary and legal system.
One consequence of the concept of private property was the evolution of a market economy, but until the innovation of money was introduced, commerce was on a barter basis. There is some debate regarding
the exact moment when money was first used, but its use revolutionized
commerce, private property, and the accumulation of wealth. It provided a new means of stockpiling resources, and thus had an important
impact on risk management. With the introduction of money as a storage
medium, wealth could be held in the form of tangible property or as an
asset that could be exchanged for tangible properties. Physical assets
could be acquired even by those who did not have financial assets, provided someone was willing to lend the money, which was the innovation
of credit. This created risk for the lender, who was compensated by
charging interest for loans.
The legal system was the second innovation that revolutionized society. Laws or rules originated as tribal conventions, which became more formalized over time. One of the first formal legal codes was established by
Hammurabi between 1792 and 1750 B.C. There were no other major legal system innovations until the beginning of the Industrial Revolution, so we can
fly over the periods of the Egyptian, Greek, and Roman empires, feudalism,
the rise of the merchant class, and mercantilism. The beginning of the Industrial Revolution was characterized by two major events. Modern capitalism emerged after a transition period over several centuries, during which
the conditions needed for a capitalistic market society were created. Among
these conditions were formalized private ownership of the means of production, profit orientation, and the mechanisms of a market economy. With
expanding industrial and economic activity, new organizational forms were
needed to raise large amounts of capital and build production capacity. The
corporation limited individual risk and leveraged production, distribution,
and capital resources. The earliest form of shareholder organization, the joint
stock company, appeared at the end of the seventeenth century. The investors
pooled their funds, allowing multiple investors to share in both the profits
and risks of the enterprise. This feature was equivalent to partnerships and
other joint forms and was not an innovation. But the corporation addressed
risk in a different way, by limiting the liability of the investors based on the
amount invested. From a legal standpoint, a corporation is an artificial construct or artificial person, whose competencies and responsibilities are separate from those of the investor-owners (with exceptions).
The Industrial Revolution created new sources of risks. The application of steam power to the production process and transportation replaced
old threats with the new risks that accompany advancing technologies.
With the emergence of the age of information technology, inherent risks
include business system problems, fraud, and privacy issues, which can
all interrupt the day-to-day operations of a business.
Although the term risk management originated in the 1950s, Henry
Fayol recognized its significance earlier.1 Fayol, a leading management
authority, was influenced by growing mass production in the United
States, and the existence of giant corporations and their management
challenges. In 1916, he structured industrial activities into six functions,
including one called security, which sounds surprisingly like the concept
of risk management:
The purpose of this function is to safeguard property and persons against
theft, fire and flood, to ward off strikes and felonies and broadly all social
disturbances or natural disturbances liable to endanger the progress and
even the life of the business. It is the master’s eye, the watchdog of the oneman business, the police or the army in the case of the state. It is generally
speaking all measures conferring security upon the undertaking and requisite peace of mind upon the personnel.2
Risk Management: A Maturing Discipline
Centuries ago, bandits and pirates threatened traders. Now hackers
are engaged in vandalism and commit electronic larceny.
The media are full of news about the perils of human-made and natural hazards. The nuclear power plant accidents at the Three Mile Island
facility in Pennsylvania in 1979 and at Chernobyl in Ukraine in 1987 show
the new risks posed by human-made hazards and the seriousness of these
threats. Destructive natural hazards exist as well. Hurricane Andrew
caused damages of around $22 billion; and the floods in the midwestern
United States in 1993 and the earthquakes in California in 1993 and in
Kobe, Japan, in 1994 had devastating effects. In addition, terrorist activities have become more dangerous over the years, as demonstrated by the
1993 and 2001 bombings of the World Trade Center in New York, and the
1995 bombing of the Murrah Federal Building in Oklahoma City.
A review of the past along with an assessment of the growing array
of risks shows that the impact of risks (in terms of financial losses) has increased. This is not only a consequence of the increased numbers of risks
we are confronted with; the severity and frequency of disasters has increased as well. The financial losses from natural perils, such as floods,
forest fires, and earthquakes, are not only a function of the number of
events, as natural disasters occur with a certain average frequency as in
the past. However, each catastrophe seems to be worse than the one that
came before it. The ultimate reason is obvious: as more and more people
live close together, business has become more capital intensive, and our
infrastructure is more vulnerable and capital intensive as well. With the
increased growth of capital investment in infrastructure, manufacturing
capacity, and private ownership of real estate and other goods, the risk of
financial losses increased substantially.
Recently, there have been a number of massive financial losses due to inadequate risk management procedures and processes (Figure 1-2). The failures of risk management in the world of finance were not primarily due to
the incorrect pricing of derivative instruments. Rather, the necessary supervisory oversight was inadequate. The decision makers in control of organizations left them exposed to risks from derivative transactions and
institutional money. Risk management does not primarily involve the correct pricing of derivative instruments—rather, it involves the supervision,
management, and control of organizational structures and processes that deal
with derivatives and other instruments.
Many cases in which managers focused on the correct pricing of
financial instruments and neglected the other dimensions show the
dramatic consequences of this one-dimensional understanding of risk
management. In Switzerland, the pension fund scheme of Landis & Gyr
F I G U R E 1-2
Overview of the Most Important and Obvious “Accidents” of the Past Decades.
Bank of Credit and Commerce
International (BCCI);
Credit Lyonnais;
Losses, $ million
LTCM; 3500
Metallgesellschaft AG;
Greenwich, CT;
Orange County, CA;
Mirror Group Pension Fund;
Cendant; 2800
Barings Bank;
Bre-X; 1200
Banco Ambrosiano and the
Vatican Bank; 1300
Drexel Burnham Lambert;
Kidder Peabody & Co.;
Daiwa Bank;
Deutsche Morgen Grenfell;
Bankers Trust; 177
NatWest 117.65
Smith Barney; 40
Jardine Flemming; 19.3
Griffin Trading Company;
Risk Management: A Maturing Discipline
resulted in the loss of a substantial part of the fund’s assets. Robert
Maxwell swindled the Mirror Group’s pension fund for £480 million.
Daiwa lost more than $1 billion. Barings lost £850 million. Kidder
Peabody lost more than $300 million. Orange County, California, lost
more than $1 billion. This list of accidents, frauds, and willful swindles
in the world of finance is never-ending. The reasons include behavioral
risk, pricing risk, an incorrect understanding of products and services,
and simple credit and market risks. Risk is not a one-dimensional, welldefined concept. Rather, it is a shifting concept whose meaning varies
according to the environment in which it is used. Thus far, the term risk
has been used in this discussion to mean “exposure to adversity.” In this
loose sense, the term risk has been adequate for the explanation of the
history of risk. Now, risk and its associated terms have to be analyzed
and defined more precisely, and the context in which these terms are
used must be outlined. Each activity or area of knowledge has its own
individual concept and terms. The terminology of risk, like many simple
terms in everyday usage, takes on different meanings in specialized
fields. The term risk shimmers with all the colors of the rainbow; it depends on how we define it. Risk is often linked with uncertainty and insecurity. Statisticians, economists, bankers, and academicians try and try
again to develop a common understanding and definition of the term
risk. But at present there is no agreed definition that can be applied to all
areas; the concept of risk that is suitable for the economist can not be
used by the social psychologist or the insurance mathematician. This
book does not attempt to develop a concept for all areas of knowledge.
The discussion is limited to economics and finance. However, there are
some concepts that are shared with the fields of insurance, mathematics,
and statistics, as many products and services in the economic and financial field are based on calculations that include risk. In the insurance industry, risk means either a peril insured against (e.g., flood damage) or a
person or property protected by insurance (e.g., a driver and vehicle
protected against financial damages from personal injury or collision by
car insurance). For the moment, however, the term risk will be applied
here in an abstract way, to indicate a situation in which a certain exposure exists. Therefore, risk is not strictly related to loss for present purposes, as this again would be one-dimensional and would unnecessarily
restrict the discussion.
For the purposes of this discussion, risk is defined as “a condition in which
there exists an exposure to adversity.” In addition, there is an expectation
of what the outcome should look like. Therefore, risk is defined here as
risk A condition in which there exists a possibility of deviation from a desired
outcome that is expected or hoped for.
Other definitions include the restriction that risk is based on realworld events, including a combination of circumstances in the external environment. We do not agree with this limitation. Potential risks that might
occur in the future are excluded. In addition, we do not limit the range of
risk to circumstances in the external environment. Many crises in the
economy and the financial services industry happen because of problems
within organizations. These often have to do with problems in the human
resource area, which belong in the realm of the behavioral sciences.
The term risk is linked to the possibility of deviation. This means that
the possibility of risk can be expressed as a probability, ranging from 0 to
100 percent. Therefore, the probability is neither impossible nor definite.
This definition does not require that the probability be quantified, only
that it must exist. The degree of risk may not be measurable, for whatever
reason, but the probability of the adverse outcome must be between 0 and
100 percent.
Another key element of the definition is the “deviation from a desired outcome that is expected or hoped for.” The definition does not say
how such an undesirable deviation is defined. There are many ways of
building expectations. By projecting historical data into the future, we
build expectations. This pattern of behavior can be observed in our everyday lives. Another way of building expectations is to forecast by using information directed toward the future, not by looking back. The definition
of expectations is absolutely key in the concept of risk, as it is used to define
the benchmark. Any misconception of the expectations will distort the
measurement of risk substantially. This issue is discussed in full in the auditing and consulting literature, which analyzes the problem of risk and
control in great depth.3
Many definitions of risk include the term adverse deviation to express
the negative dimension of the expected or hoped-for outcome. We do not
agree with this limitation, which implies that risk exists only with adverse
deviations, which must be negative and thus are linked to losses. Such a
restriction would implicitly exclude any positive connotations from the
concept of risk. We believe that risk has two sides, which both have to be
included in the definition, and that risk itself has no dimension, negative
or positive.
Frequently, terms such as peril, hazard, danger, and jeopardy are used interchangeably with each other and with the term risk. But to be more precise
about risk, it is useful to distinguish these terms:
Risk Management: A Maturing Discipline
Peril. A peril creates the potential for loss. Perils include floods,
fire, hail, and so forth. Peril is a common term to define a danger
resulting from a natural phenomenon. Each of the events
mentioned is a potential cause of loss.
Hazard. A hazard is a condition that may create or increase the
chance of a loss arising from a given peril. It is possible for
something to be both a peril and a hazard at the same time. For
instance, a damaged brake rotor on a car is a peril that causes an
economic loss (the brake has to be repaired, causing financial
loss). It is also a hazard that increases the likelihood of loss from
the peril of a car accident that causes premature death.
Hazards can be classified into the following four main categories:
Physical hazard. This type of hazard involves the physical
properties that influence the chances of loss from various perils.
Moral hazard. This type of hazard involves the character of
persons involved in the situation, which might increase the
likelihood of a loss. One example of a moral hazard is the dishonest
behavior of a person who commits fraud by intentionally
damaging property in order to collect an insurance payment. This
dishonest behavior results in a loss to the insurance company.
Morale hazard. This type of hazard involves a careless attitude
toward the occurrence of losses. An insured person or
organization, knowing that the insurance company will bear the
brunt of any loss, may exercise less care than if forced to bear any
loss alone, and may thereby cause a condition of morale hazard,
resulting in a loss to the insurance company. This hazard should
not be confused with moral hazard, as it requires neither
intentional behavior nor criminal tendencies.
Legal hazard. This type of hazard involves an increase in the
severity and frequency of losses (legal costs, compensation
payments, etc.) that arises from regulatory and legal requirements
enacted by legislatures and self-regulating bodies and interpreted
and enforced by the courts. Legal hazards flourish in jurisdictions
in which legal doctrines favor a plaintiff, because this represents a
hazard to persons or organizations that may be sued. The American
and European systems of jurisprudence are quite different. In the
American system, it is much easier to go to court, and producers of
goods and services thus face an almost unlimited legal exposure to
potential lawsuits. The European courts have placed higher hurdles
in the path of those who might take legal action against another
party. In addition, “commonsense” standards of what is actionable
are different in Europe and the United States.
For a risk manager, the legal and criminal hazards are especially important. Legal and regulatory hazards arise out of statutes and court decisions. The hazard varies from one jurisdiction to another, which means
global companies must watch legal and regulatory developments carefully.
Risk itself does not say anything about the dimension of measurement.
How can we express that a certain event or condition carries more or less
risk than another? Most definitions link the degree of risk with the likelihood of occurrence. We intuitively consider events with a higher likelihood of occurrence to be riskier than those with a lower likelihood. This
intuitive perception fits well with our definition of the term risk. Most definitions regard a higher likelihood of loss to be riskier than a lower likelihood. We do not agree, as this view is already affected by the insurance
industry’s definition of risk. If risk is defined as the possibility of a deviation from a desired outcome that is expected or hoped for, the degree of
risk is expressed by the likelihood of deviation from the desired outcome.
Thus far we have not included the size of potential loss or profit in
our analysis. We say that a situation carries more or less risk, and mean as
well the value impact of the deviation. The expected value of a loss or
profit in a given situation is the likelihood of the deviation multiplied by
the amount of the potential loss or profit. If the money at risk is $100 and
the likelihood of a loss is 10 percent, the expected value of the loss is $10.
If the money at risk is $50 and the likelihood of a loss is 20 percent, the expected value of the loss is still $10. The same calculation applies to a profit
situation. This separation of likelihood and value impact is very important, but we do not always consider this when we talk about more or less
risk. Later we will see how the separation of likelihood and impact can
help us analyze processes, structures, and instruments to create an overall
view of organizational risk.
Frequently, persons who sit on supervisory committees (e.g., board
members and trustees of endowment institutions and other organizations) have to make decisions with long-ranging financial impact but have
inadequate backgrounds and training to do so. Organizational structures
and processes are rarely set up to support risk management, as these
structures are usually adopted from the operational areas. But with increased staff turnover, higher production volumes, expansion into new
markets, and so forth, the control structures and processes are rarely
adapted and developed to match the changing situation.
New problems challenge management, as the existing control
processes and reporting lines no longer provide alerts and appropriate information to protect the firm from serious damage or bankruptcy, as was
the case with Barings or Yamaichy.
Risk Management: A Maturing Discipline
Banks and other regulated financial institutions have been forced by
government regulations and industry self-regulating bodies to develop
the culture, infrastructure, and organizational processes and structures for
adequate risk management. Risk management has become a nondelegable
part of top management’s function and thus a nondelegable responsibility
and liability. Driven by law, the financial sector has developed over the
past years strategies, culture, and considerable technical and management
know-how relating to risk management, which represents a competitive
advantage against the manufacturing and insurance sectors.
1.6.1 Background
As previously discussed, risk management is a shifting concept that has
had different definitions and interpretations. Risk management is basically a scientific approach to the problem of managing the pure risks faced
by individuals and institutions. The concept of risk management evolved
from corporate insurance management and has as its focal point the possibility of accidental losses to the assets and income of the organization.
Those who carry the responsibility for risk management (among whom
the insurance case is only one example) are called risk managers. The term
risk management is a recent creation, but the actual practice of risk management is as old as civilization itself. The following is the definition of
risk management as used used throughout this work:
risk management In a broad sense, the process of protecting one’s person or organization intact in terms of assets and income. In the narrow sense, it is the managerial function of business, using a scientific approach to dealing with risk. As such,
it is based on a distinct philosophy and follows a well-defined sequence of steps.
1.6.2 History of Modern Risk Management
Risk management is an evolving concept and has been used in the sense defined here since the dawn of human society. As previously mentioned, risk
management has its roots in the corporate insurance industry. The earliest
insurance managers were employed at the turn of the twentieth century by
the first giant companies, the railroads and steel manufacturers. As capital
investment in other industries grew, insurance contracts became an increasingly significant line item in the budgets of firms in those industries, as well.
It would be mistaken to say that risk management evolved naturally
from the purchase of insurance by corporations. The emergence of risk
management as an independent approach signaled a dramatic, revolu-
tionary shift in philosophy and methodology, occurring when attitudes
toward various insurance approaches shifted. One of the earliest references to the risk management concept in literature appeared in 1956 in the
Harvard Business Review.4 In this article, Russell Gallagher proposed a revolutionary idea, for the time, that someone within the organization should
be responsible for managing the organization’s pure risk:
The aim of this article is to outline the most important principles of a workable program for “risk management”—so far so it must be conceived, even
to the extent of putting it under one executive, who in a large company
might be a full-time “risk manager.”
Within the insurance industry, managers had always considered insurance to be the standard approach to dealing with risk. Though insurance
management included approaches and techniques other than insurance
(such as noninsurance, retention, and loss prevention and control), these approaches had been considered primarily as alternatives to insurance.
But in the current understanding, risk management began in the early
1950s. The change in attitude and philosophy and the shift to the risk management philosophy had to await management science, with its emphasis on
cost-benefit analysis, expected value, and a scientific approach to decision
making under uncertainty. The development from insurance management
to risk management occurred over a period of time and paralleled the evolution of the academic discipline of risk management (Figure 1-3). Operations
research seems to have originated during World War II, when scientists were
engaged in solving logistical problems, developing methodologies for deciphering unknown codes, and assisting in other aspects of military operations. It appears that in the industry and in the academic discipline the
development happened simultaneously, but without question the academic
discipline produced valuable approaches, methodologies, and models that
supported the further development of risk management in the industry.
New courses such as operations research and management science emphasize the shift in focus from a descriptive to a normative decision theory.
Markowitz was the first financial theorist to explicitly include risk in
the portfolio and diversification discussion.5 He linked terms such as return
and utility with the concept of risk. Combining approaches from operations
research and mathematics with his new portfolio theory, he built the basis
for later developments in finance. This approach became the modern portfolio theory, and was followed by other developments, such as Fischer Black’s
option-pricing theory, which is considered the foundation of the derivatives industry. In the early 1970s, Black and Scholes made a breakthrough
by deriving a differential equation which must be satisfied by the price of
any derivative instrument dependent on a nondividend stock.6 This approach has been developed further and is one of the driving factors for the
actual financial engineering of structured products.
Risk Management: A Maturing Discipline
F I G U R E 1-3
Evolution of Insurance and Risk Management.
Roots: Classical insurance
WW II: Development of operations research
1950s: Evolution of operations research and
management sciences as academic subjects
Extreme value orientation
Loss/cost orientation
Risk management,
quantitatively oriented
Risk management,
cost / management oriented
Cost accounting
Management sciences
Portfolio optimization
Option pricing
Return / risk relation
+ Link to accounting
+ Management (organization,
+ Portfolio approach
+ Instrument valuation
+ Models / methodology
- Lack of models
- Lack of methodological
- Link to accounting missing
- Link to processes missing
Trend: Combining the approaches
to generate the methodological basis
of an enterprisewide risk management
The current trend in risk management is a convergence of the differing
approaches, as both trends have positive aspects (see Figure 1-4). Almost all
leading consulting practices have developed value-at-risk concepts for enterprisewide risk management. Process pricing is the ultimate challenge for
the pricing of operational risk.
of risk
of risk
Linking risk
and return
Risk management sophistication
Control of risk
Development Levels of Different Risk Categories.
F I G U R E 1-4
Shareholder value objective
Strategic advantage
Risk Management: A Maturing Discipline
Related Approaches Total Risk Management
Total risk management, enterprisewide risk management, integrated risk management, and other terms are used for approaches that implement
firmwide concepts including measurement and aggregation techniques
for market, credit, and operational risks. This book uses the following definition for total risk management, based on the understanding in the market regarding the concept:
total risk management The development and implementation of an enterprisewide risk management system that spans markets, products, and processes
and requires the successful integration of analytics, management, and technology.
The following paragraphs highlight some concepts developed by
consulting and auditing companies. Enterprise risk management, as developed by Ernst & Young, emphasizes corporate governance as a key element
of a firmwide risk management solution. Boards that implement leadingedge corporate governance practices stimulate chief executives to sponsor
implementation of risk management programs that align with their businesses. In fulfilling their risk oversight duties, board members request regular updates regarding the key risks across the organization and the
processes in place to manage them. Given these new practices, boards are
increasingly turning to the discipline of enterprise risk management as a
means of meeting their fiduciary obligations. As a result, pioneering organizations and their boards are initiating enterprisewide risk management programs designed to provide collective risk knowledge for effective
decision making and advocating the alignment of management processes
with these risks. These organizations have recognized the advantages of:
Achieving strategic objectives and improving financial
performance by managing risks that have the largest potential
Assessing risk in the aggregate to minimize surprises and reduce
earnings fluctuations
Fostering better decision making by establishing a common
understanding of accepted risk levels and consistent monitoring
of risks across business units
Improving corporate governance with better risk management
and reporting processes, thereby fulfilling stakeholder
responsibilities and ensuring compliance with regulatory
At present, many risk management programs attempt to provide a
level of assurance that the most significant risks are identified and man-
aged. However, they frequently fall short in aggregating and evaluating
those risks across the enterprise from a strategic perspective. Effective enterprise risk management represents a sophisticated, full-fledged management discipline that links risk to shareholder value and correlates with
the complexity of the organization and the dynamic environments in
which it operates (Figure 1-5).
Once an organization has transformed its risk management capabilities, it will be in a position to promote its success through an effective, integrated risk management process. Ernst & Young’s point of view is that
effective enterprise risk management includes the following points (see
Figure 1-6):7
A culture that embraces a common understanding and vision of
enterprise risk management
A risk strategy that formalizes enterprise risk management and
strategically embeds risk thinking within the enterprise
F I G U R E 1-5
Evolving Trends and the Development of an Integrated Risk Framework to Support
the Increasing Gap Between Business Opportunities and Risk Management Capabilities. (Source: Ernst & Young, Enterprise Risk Management, Ernst & Young LLP,
2000. Copyright © 2000 by Ernst & Young LLP; reprinted with permission of Ernst
& Young LLP.)
Risk Management: A Maturing Discipline
F I G U R E 1-6
Enterprise Risk Management Point of View. (Source: Ernst & Young LLP, a member of Ernst & Young Global. Copyright © 2002 by Ernst & Young LLP; reprinted
with permission of Ernst & Young LLP.)
ri s
r evi
pro nagem
ces ent
risk st rategy
cap re an
abi d
l it y
supp d and
t echnol ogy
value based
age ns
ma t io
sk f unc
An evolved governance practice that champions an effective
enterprisewide risk management system
Competent and integrated risk management capabilities for
effective risk identification, assessment, and management
Coopers & Lybrand has developed its own version of an enterprisewide risk management solution in the form of generally accepted risk
principles (GARP).8 The GARP approach seeks to distil and codify major
principles for managing and controlling risk from the guidance issued to
date by practitioners, regulators, and other advisors. The framework uses
the experience and expertise of all parties involved in its development to
expand these principles so as to establish a comprehensive framework
within which each firm can manage its risks and through which regulators
can assess the adequacy of risk management in place. It presents a set of
principles for the management of risk by firms, and for the maintenance of
a proper internal control framework, going further than the mere assessment of the algorithms within risk management models. It covers such
matters as the organization of the firm, the operation of its overall control
framework, the means and principles of risk measurement and reporting,
and the systems themselves. The approach is based around principles, each
of which is supported by relevant details. The extent of the detail varies
depending on the principle concerned. In all cases, the guidance provided
is based on the assumption that the level of trading in a firm is likely to
give rise to material risks. In certain cases an indication of alternative acceptable practices is given.
KPMG has developed a risk management approach based on the
shareholder value concept, in which the value of an organization is not
solely dependent on market risks, such as interest or exchange rate fluctuations. It is much more important to study all types of risks. This
means that macroeconomic or microeconomic risks, on both the strategic
and operational levels, have to be analyzed and considered in relation to
every single decision. An organization can seize a chance for lasting and
long-term success only if all risks are defined and considered in its overall
decision-making process as well as in that of its individual business
units. KPMG assumes (as do other leading companies) that the key factor for a total risk management approach is the phase of risk identification, which forms the basis for risk evaluation, risk management, and
control. Figure 1-7 shows the Risk Reference Matrix, KPMG’s systematic
and integrated approach to the identification of risk across all areas of
the business.9 This is a high-level overview, which can be further broken
down into details.
Many other approaches from leading consulting and auditing practices could be mentioned. They all assume that they have a framework
that contains all the risks that must be identified and measured to get the
overall risk management.
Figure 1-8 shows a risk map that covers many different risk areas,
from a high-level to low-level view. From an analytical standpoint, it looks
consistent and comprehensive, covering all risks in an extended framework. The allocation of individual risks may be arbitrary, depending on
what concept is used. But the combination and complexity of all risks,
their conditions and assumptions, might make it difficult to identify and
measure the risk for an enterprisewide setup.
In practice, significant problems often occur at this stage. A systematic and consistent procedure to identify risk across all areas of the business, adhering to an integrated concept, is essential to this first sequence
of the risk management process. But this integrated concept is, in certain
regards, a matter of wishful thinking. The definition of certain individual
risks—for example, development, distribution, and technology risks—is
not overly problematic. The concepts span the complete range of risk
terms. But in many cases the categorization and definition of some terms
are ambiguous. One example is the term liquidity. Liquidity can be seen as
Risk Management: A Maturing Discipline
F I G U R E 1-7
KPMG Risk Reference Matrix. (Source: Cristoph Auckenthaler and Jürg Gabathuler,
Gedanken zum Konzept eines Total Enterprise Wide Risk Management (TERM), Zurich:
University of Zurich, 1997, 9, fig. 2.)
Risk Factors
Environment Risk
Risk Factors
Stability Risk
National Stability
General IndustryRelated Risks
Local Industrial
Sector Risks
Ethical Value
Business Value
Business Policy
Activity Risk
Outside Risk
Policy Risks
Development &
Production Risks
Financial Market
Support Service
part of market and credit risks, but it also affects systemic risk. The total
risk management concept appears to be complete, consistent, and adequate. But this interpretation is too optimistic, as some of the concepts still
lack major elements and assumptions.
In an overall approach, the interaction between individual risks, as
well as the definition of the weighting factors between the risk trees that
must be attached to this correlation, creates serious difficulties. Portfolio
theory tells us that correlation between the individual risk elements rep-
F I G U R E 1-8
Risk Map of a Total Risk Management Approach. (Source: Modified from KPMG.)
Systemic risk
management /
Communication / relationship
Corporate strategy /
Management direction and
decision making
Human resources
selling /
Product / service
External physical
Financial risk
Operational risk
Systemic risk
Strategic / management risk
Credit risk
Market risk
Internal physical
Risk Management: A Maturing Discipline
resents a central role in the establishment of risk definitions and strategies, and therefore in the risk management and hedging process (provided hedging is feasible). The same is also true for the risk management
of a business (with elements such as new product risks, model risks,
counterparty risks, etc.). From a practical standpoint, it is often not possible to get data and calculate risk coefficients if the overall scheme of a
total risk management concept represents a widely branching system,
because the number of interactions (correlations) and the required data
increase substantially as the number of elements increases. Such approaches require the combined and well-orchestrated use of questionnaires, checklists, flowcharts, organization charts, analyses of yearly
financial statements and transactions, and inspections of the individual
business locations. This requires substantial expenditures and commitment from management.
As can be seen from the preceding descriptions of the different enterprise risk management solutions, the major consulting firms approach
the same issues from different perspectives. Whereas KPMG and Ernst &
Young have a more holistic approach, Coopers & Lybrand takes a more
normative, trading-oriented, and regulatory approach. Regardless of the
different approaches offered by the various auditing and consulting companies, a company has to adapt the approach it selects based on its own
needs, its understanding of risk management, and the extent to which risk
management is an integrated part of upper management’s responsibilities
or an independent control and oversight function. Total Quality Management
Virtually every activity within an organization changes the organization’s exposure to risk. It is part of a risk manager’s responsibility to educate others on the risk-creating and risk-reducing aspects of their
activities. The recognition that risk control is everyone’s responsibility
closely links risk control to principles of quality improvement, an approach to management that has been employed with considerable success in Japan and the United States. The movement toward quality
improvement often is known by code names and acronyms such as total
quality management (TQM) and total quality improvement (TQI). TQM was
developed in Japan after World War II, with important contributions
from American experts. Ultimately, Japanese companies recognized that
production volume itself does not create competitive advantage, only
quality and product differentiation can do so. In the context of TQM,
quality is here defined as follows:10
quality The fulfillment of the agreed-upon requirements communicated by the
customer regarding products, services, and delivery performance. Quality is
measured by customer satisfaction.
TQM has five approaches, reflecting the different dimensions of
Transcendent approach. Quality is universally recognizable and is
a synonym for high standards for the functionality of a product.
The problem is that quality cannot be measured precisely under
this approach.
Product-oriented approach. Differences in quality are observable
characteristics linked to specific products. Thus, quality is
precisely measurable.
User-oriented approach. Quality is defined by the user, depending
on the utility value.
Process-oriented approach. The production process is the focus of
quality efforts. Quality results when product specifications and
standards are met through the use of the proper production
Value-oriented approach. Quality is defined through the priceproduct-service relationship. A quality product or service is
identified as one that provides the defined utility at an acceptable
The TQM approach has four characteristics:
Zero-error principle. Only impeccable components and perfect
processes may be used in the production process to ensure
systematic error avoidance in the quality circle.
Method of “why.” This is a rule of thumb: the basis of a problem
can be evaluated by asking why five times. This avoids taking the
symptoms of a problem to be the problem itself.
Kaizen. Kaizen is a continuous process of improvement through
systematic learning. This means turning away from the traditional
tayloristic division of labor and returning to an integrated
organization of different tasks that includes continuous training to
develop personnel’s technical and human relations skills.
Simultaneous engineering. Simultaneous engineering demands
feedback loops between different organizational units and
different processes. This requires overlapping teams and process
Table 1-1 highlights the profiles of the total quality management and
total risk management approaches.
Total quality management has its own very distinct terms and definitions, which make it a different approach from total risk management. It
is a multidimensional client-oriented approach, in which management
takes preventive measures to ensure that all processes, organizational en-
Risk Management: A Maturing Discipline
T A B L E 1-1
Differences and Similarities Between Total Quality Management
and Total Risk Management
Total Quality Management (TQM)
Total Risk Management (TRM)
Extended, multidimensional, clientoriented quality term.
Integrated, multidimensional enterpriseoriented term.
Extended client definition: clients are
internal and external.
Internal client definition: clients are
Preventive quality assurance policy.
Preventive and product-oriented risk
management policy.
Quality assurance is the duty of all
TRM assurance is the duty of specially
assigned and responsible persons.
Enterprisewide quality assurance.
TRM assurance within the limits and for
the risk factors to be measured according
to the risk policy.
Systematic quality improvement with
zero-error target.
Systematic risk control within the
defined limits.
Quality assurance is a strategic job.
TRM is a strategic job.
Quality is a fundamental goal of the
TRM is a fundamental goal of the
Productivity through quality.
TRM to ensure ongoing production.
SOURCE: Hans-Jörg Bullinger, “Customer Focus: Neue Trends für eine zukunftsorientierte Unternehmungsführung,” in
Hans-Jörg Bullinger (ed.), “Neue Impulse für eine erfolgreiche Unternehmungsführung, 13. IAO-Arbeitstagung,” Forschung
und Praxis, Band 43, Heidelberg u.a., 1994.
tities, and employees focus on quality assurance and continuous improvement throughout the organization.
1.6.4 Approach and Risk Maps
Figures 1-9 and 1-10 present the approach and risk maps used in this book.
There is no uniform accepted definition of systemic risk. This book uses
the definition contained in a 1992 report of the Bank for International Settlement (BIS):13
F I G U R E 1-9
Risk Categorization Used as an Integrative Framework in This Book.
Model Risk
Equity Price Risk
Equity Risk
Product Risk
Model Risk
Interest Rate Risk
Market Risk Factors
Currency Risk
Commodity Risk
Basis / Spread Risk
Product Risk
Model Risk
Fx Curve Risk
Basis / Spread Risk
Commodity Curve
Liquidity Risk
Model Risk
Capital Adequacy
Model Risk
Risk Disclosure
Regulatory Constraints
Current Exposure
Counterparty Risk
Potential Exposure
Cumulation Risk
Direct Credit Risk
Credit Risk Exposure
Credit Equivalent
Credit Risk
Model Risk
Diversification Risk
Capital Adequacy
Model Risk
Risk Disclosure
Regulatory Constraints
Product / Market
Sales Risks
Order Capture &
Customer / Transaction
Marketing Risks
Business Control
Internal Audit
Operational Risk
Legal & Compliance
Support Service Risks
IT / Technology
Risk Disclosure
Regulatory Constraints
Political Stability
International / National
Stability Risks
Legal System
Systemic Risk
Market Access /
Market Efficiency
Market Liquidity
Yield Curve Risk
Model Risk
Market Risk
Basis / Spread Risk
F I G U R E 1-10
Example of Transaction Breakdown, Process-Oriented Flow of Different Risk Categories Involved.
Market Risk
Market Risk
Credit Risk
Credit Risk
Trade Management
Order Routing
Trade Execution
Settlement and
Custody or
Securities Lending
Market Risk
Market Risk
Credit Risk
Legal /
Legal /
Systemic Risk
During the phases of research, tactical or
strategic asset allocation, and selection of
instruments, there is an inherent risk of
misjudgment or faulty estimation.
Therefore, timing, instrument selection,
and rating considerations have a market
and credit component.
Compliance has to take
into account all client
restrictions, internal
directives, and
regulatory constraints
affected by the intended
transaction. Capital
adequacy, suitability to
the client's account, and
so forth, also must be
From the moment the trade is entered into the system until the final transaction is entered in the portfolio accounting and custody or
securities lending systems, systems are crucial and have inherent risks.
During the trade execution phase, the trading desk has directed exposure to system risk. Until final settlement, the trade amount is
exposed to disruption in the system, which could disturb correct trade confirmation and settlement.
From the moment of execution until settlement, the books are exposed to changes in the market risk factors. They are also exposed to
changes in spread risk (i.e., credit risk).
Market risk during the trade execution is especially high, as the market price or model pricing might give the wrong information (e.g., the
market could be illiquid, or the models might not fit the instruments).
Compliance can be
considered the last stop
before the transaction is
complete. There is the
opportunity to review
whether the transaction
has been executed and
settled correctly.
systemic risk The risk that a disruption (at a firm, in a market segment, to a settlement system, etc.) causes widespread difficulties at other firms, in other market
segments, or in the financial system as a whole.
In this definition, systemic risk is based on a shock or disruption originating
either within or outside the financial system that triggers disruptions to
other market participants and mechanisms. Such a risk thereby substantially impairs credit allocation, payments, or the pricing of financial assets.
While many would argue that no shock would be sufficient to cause a total
breakdown of the financial system, there is little doubt that shocks of substantial magnitude could occur, and that their rapid propagation through
the system could cause a serious system disruption, sufficient to threaten the
continued operation of major financial institutions, exchanges, or settlement
systems, or result in the need for supervisory agencies to step in rapidly.
1.7.2 Causes of Systemic Risk
Under the BIS definition, one should consider not only the steps taken
within the institution to guard against a major internal breakdown. One
should also consider those features of the global financial marketplace
and current approaches to risk management and supervision that could
adversely affect the institution’s ability to react quickly and appropriately
to a shock or disturbance elsewhere.
Recent developments in the financial market have produced a broad
range of highly developed pricing models. Shareholder value, which is often
mistakenly thought of as the generation of higher return on equity, leads financial institutions to reduce the proprietary capital used for activities that increase the profitability of equity capital. The financial institution reduces the
equity capital to the bare regulatory minimum with the result that less and less
capital supports the expanded trading activities, because the shareholder
value concept has nothing to do with capital support. This trend is quite
dangerous, as less and less capital serves as security capital in the returngeneration process for more and more risk, without generating commensurate
returns, and this trend alone promotes systemic risks. The development of an
internationally linked settlement system has progressed significantly; nevertheless, there are still other factors that create systemic risk.
1.7.3 Factors That Support Systemic Risk
The following factors support systemic risk, based on empirical experience from previous crises or near-misses in the market:
Economic implications. Our understanding of the relationship
between the financial markets and the real state of the economy is
Risk Management: A Maturing Discipline
questionable. The pricing of individual positions or positions for a
portfolio can be done with any desired precision. The economic
implications of the created models are often overlooked. It is not
always a simple matter to understand the basic economic
assumptions and parameters of complex mathematical models.
This is one of the biggest systemic risks and a possible reason for
the irritating, erratic movements of the markets. The participants—
especially the “rocket scientists,” highly intelligent but with a
narrow horizon—do not understand the impact of coordination
and feedback loops among the many individual decisions on the
financial markets, especially concerning derivative constructs.
Liquidity. Pricing models work under the ideal assumption that
markets are liquid. Even worst-case scenarios and stress testing of
market situations assume liquid markets. Valuation models are
still hedge and arbitrage models, and are always based on the
assumptions that positions can be liquidated and cash positions
can be adjusted. With illiquid markets, strategy changes or
position liquidation are difficult and sometimes impossible. Such
a situation might cause a domino effect—an institution trying to
liquidate positions in an illiquid market experiences cash
problems, which causes the market to react negatively, sweeping
away other institutions. The LTCM case is a typical example of
this kind of systemic risk exposure (see case study in Chapter 6).
It is important to distinguish between liquidity risk as part of systemic risk and liquidity risk as part of market and credit risk. Market liquidity risk as part of systemic risk relates to the market itself, not to the
pricing of individual positions.
The over-the-counter (OTC) market is a very attractive market for financial institutions, as the margins in this market are higher than on
traded exchanges. The volume in the OTC market is enormous, but nontransparent. Transactions are not subject to the same clearing, settlement,
and margin requirements as on traded exchanges. The risk of the OTC
market, then, is that it is nontransparent, noninstitutionalized, and almost
unregulated. Surprises may appear out of nowhere, and they may cause
quick market reactions, disrupting the financial system with feedback
loops and affecting financial institutions.
1.7.4 Regulatory Mechanisms
for Risk Management
The regulatory bodies have recognized the need for adequate risk measurement and management techniques and approaches. The toolbox of the
regulators is not limited to quantitative models, as many accidents and
near-misses have highlighted the need for transparency and disclosure of
market, credit, and operational risk information. A well-informed investor
is well positioned to adjust the price based on available information, reflecting the expected risk premium for the entity being invested in.
Minimum disclosure requirements, risk management and control
guidance through local supervisors, cross-border coordination of local
regulators, and shared control of supranational organizations are some of
the options regulators can select to keep systemic risk under control. The
following topics highlight the focus of regulations recently published by
BIS, and also indicate the mindset of the regulators, based on some recent
Enhancing Bank Transparency, September 1998. Public disclosure
and supervisory information that promote safety and soundness
in banking systems.14
Supervisory Information Framework for Derivatives and Trading
Activities, September 1998. Joint Report by the Basel Committee
on Banking Supervision and the Technical Committee of the
International Organization of Securities Commissions (IOSCO).15
Framework for Internal Control Systems in Banking Organisations,
September 1998.16
Essential Elements of a Statement of Cooperation Between Banking
Supervisors, May, 2001. Framework for cross-border cooperation
among different local regulators.17
Conducting a Supervisory Self-Assessment: Practical Application,
April 2001; The Relationship Between Banking Supervisors and Banks’
External Auditors, February 2001. Guidelines for local regulators
to assess their own supervisory abilities and the national
supervisory frameworks.18
Best Practices for Credit Risk Disclosure, September 2000; Industry
Views on Credit Risk Mitigation, January 2000; Range of Practice in
Banks’ Internal Ratings Systems, January 2000. Reviews of current
best practices for credit risk disclosures, which became part of the
new capital adequacy framework to increase the quality level of
disclosed information and generate peer pressure.19
Review of Issues Relating to Highly Leveraged Institutions, March
2001; Banks’ Interactions with Highly Leveraged Institutions, January
2000. Reviews and recommendations regarding banks’ exposure
and transactions with highly leveraged institutions, based on the
LTCM crisis of September 1998.20
The approach of the BIS regulations is clearly a combination of the
various measures available to the supervisory organizations, designed to
avoid systemic risks and protect clients through increased disclosure and
Risk Management: A Maturing Discipline
transparency and more precise calculation of the capital needed to support risks.
None of the previously mentioned approaches would achieve these
objectives on their own. Thus, the new capital adequacy approach integrates the different risk categories and the different supervisory tools in
the form of capital adequacy calculation, disclosure requirements, crossborder cooperation among supervisors, and the like.
Risk management is not a new function or gadget in the financial industry.
However, based on recent events, regulators and the media have increasingly scrutinized risk management practices and techniques. A closer look
at some of the accidents makes it apparent that managers, regulators, and
investors have partially lost control of risk management, overestimated
their own capabilities and capacities, and brought companies and entire
markets to the edge of the abyss.
For well over 100 years, farmers, for example, have engaged in risk
management as they have sought to hedge their crops against price fluctuations in commodity markets. Their preferred strategy has been to sell
short some or all of their anticipated crops before harvest time to another
party on what are called futures markets. The Chicago Board of Trade
(CBOT) was the first exchange to offer futures contracts. This strategy
guarantees the farmer a known price for a crop, regardless of what the
commodity’s future price turns out to be when the crop is harvested. Risk
management along these lines makes sense for farmers for at least two
reasons. First, agricultural prices are exposed to volatility. Many of these
farmers are not diversified and must also borrow in order to finance their
crops. Therefore, setting the future sale price now migrates the risk of
price fluctuations.
For another example that demonstrates the same approach, consider
a large aluminum extraction company, owned by numerous shareholders,
facing similar commodity price risk. For concreteness, consider a firm primarily engaged in the extraction and sale of raw aluminum on a global
basis. Given that aluminum prices are relatively volatile and are exposed
to global economic cycles, the first rationale for risk management might
seem similar to the farmer’s. However, unlike the farmer’s circumstance,
this firm is owned by a large number of shareholders, who can, if they
wish, greatly reduce or eliminate their risk from low aluminum prices
simply by holding a diversified portfolio that includes only a small fraction of assets invested in the aluminum extraction company. More generally, if investors can freely trade securities in many firms, they can choose
their exposure to volatility in aluminum prices. Indeed, in two studies,
Modigliani and Miller21 showed that, in a world with no transactions costs
or taxes and with equal information, managers could not benefit their
shareholders by altering the risk profile of the firm’s cash flow. Essentially,
in this situation, shareholders can already do whatever they choose at no
cost; actions by managers are redundant.
Although the Modigliani and Miller studies considered the options
of changing the firm’s risk profile only through the use of debt financing
(1958),22 or the distribution (or lack thereof) of dividends (1961),23 and not
through the use of financial derivative securities, the powerful implication
here is the same as that outlined earlier.
However, the practical world is not without transaction costs and
not as transparent as academic assumptions would have it. Several times
over the past decades, investors and the market have been surprised by
the announcement that a company has incurred substantial losses through
speculation, fraud, or money laundering, leaving investors with dramatically devalued investments or even in bankruptcy. No risk management
strategy as proposed by Miller and Modigliani could have prevented such
a disaster, as shareholders were unable to take any action to offset or mitigate the risks.
Regulators have become more active over the past decades and have
launched several initiatives regarding credit, market, and operational risks,
forcing financial organizations to invest in their infrastructure, processes,
and knowledge bases. The objective of both management and the regulators is to build and enforce an integrated risk management framework.
However, although the objective might be the same, the strategy is completely different from the regulatory and management viewpoints, which
is why risk management has become a hot issue. Management seeks to
protect clients’ assets at the lowest possible cost by avoiding losses and by
increasing the value of the shareholders’ investment through business decisions that optimize the risk premium. Regulators seek to protect the
clients’ assets without regard to cost, maintaining market stability and protecting the financial market by excluding systemic risk.
Risk management has to serve both purposes and thus has to be
structured, built, and managed in such a way that it can answer these different needs simultaneously. The models and approaches used in the different risk categories must give statements about the risk exposures and
allow aggregation of risk information across different risk categories. It is
the purpose of this book to look into the different models and analyze the
compatibility, assumptions, and conditions between the different models
and risk categories.
1. Henri Fayol, General and Industrial Management, New York: Pitman, 1949.
English translation of book originally published in French in 1916.
Risk Management: A Maturing Discipline
2. Ibid.
3. KPMG Peat Marwick, Understanding Risks and Controls: A Practical Guide,
Amsterdam: KPMG International Audit and Accounting Department, March
4. Russell B. Gallagher, “Risk Management: A New Phase of Cost Control,”
Harvard Business Review (September–October 1956).
5. Harry M. Markowitz, “Portfolio Selection (1),” Journal of Finance 7 (March
1952), 77–91. This is a path-breaking work in the field.
6. Fischer Black and Myron Scholes, “The Pricing of Options and Corporate
Liabilities,” Journal of Political Economy 81 (May–June 1973), 637–654.
7. Ernst & Young, Enterprise Risk Management, New York: Ernst & Young LLP,
2000; Enterprise Risk Management—Implications for Boards of Directors, New
York: Ernst & Young LLP, 2000.
8. Coopers & Lybrand, GARP—Generally Accepted Risk Principles, London:
Coopers & Lybrand, January 1996.
9. Christoph Auckenthaler and Jürg Gabathuler, Gedanken zum Konzept eines Total
Enterprise Wide Risk Management (TERM), Zurich: University of Zurich, 1997.
10. Philip B. Crosby, Qualität bringt Gewinn, Hamburg: McGraw-Hill, 1986.
11. David A. Garvin, Managing Quality, New York: Free Press, 1988.
12. Hans-Jörg Bullinger, Joachim Warschaft, Stefan Bendes, and Alexander
Stanke, “Simultaneous Engineering,” in E. Zahn (ed.), Handbuch
Technologiemanagement, Stuttgart: Schäffer-Pöschel Verlag, 1995.
13. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Delivery Versus Payment in Security Settlement Systems, Basel,
Switzerland: Bank for International Settlement, September 1992.
14. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Enhancing Bank Transparency, Basel, Switzerland: Bank for
International Settlement, September 1998.
15. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Supervisory Information Framework for Derivatives and Trading
Activities: Joint Report by the Basel Committee on Banking Supervision and the
Technical Committee of the International Organisation of Securities Commissions,
Basel, Switzerland: Bank for International Settlement, September 1998;
Trading and Derivatives Disclosures of Banks and Securities Firms: Joint Report by
the Basel Committee on Banking Supervision and the Technical Committee of the
International Organisation of Securities Commissions, Basel, Switzerland: Bank
for International Settlement, December 1988; Risk Concentrations Principles:
Joint Report by the Basel Committee on Banking Supervision, the International
Organisation of Securities Commissions, and the International Association of
Insurance Supervisors, Basel, Switzerland: Bank for International Settlement,
December 1999.
16. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Framework for Internal Control Systems in Banking Organisations,
Bank for International Settlement, Basel, Switzerland, September 1998.
17. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Essential Elements of a Statement of Cooperation Between Banking
Supervisors, Basel, Switzerland: Bank for International Settlement, May 2001.
18. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Conducting a Supervisory Self-Assessment: Practical Application,
Basel, Switzerland: Bank for International Settlement, April 2001; The
Relationship Between Banking Supervisors and Banks’ External Auditors:
Consultative Document, Issued for Comment by 12 June 2001, Basel,
Switzerland: Bank for International Settlement, February 2001.
19. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Best Practices for Credit Risk Disclosure, Basel, Switzerland: Bank
for International Settlement, September 2000; Industry Views on Credit Risk
Mitigation, Basel, Switzerland: Bank for International Settlement, January
2000; Range of Practice in Banks’ Internal Ratings Systems: Discussion Paper,
Basel, Switzerland: Bank for International Settlement, January 2000.
20. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Review of Issues Relating to Highly Leveraged Institutions, Basel,
Switzerland: Bank for International Settlement, March 2001; Banks’
Interactions with Highly Leveraged Institutions: Implementation of the Basel
Committee’s Sound Practices Paper, Basel, Switzerland: Bank for International
Settlement, January 2000.
21. M. H. Miller and F. Modigliani, “Dividend Policy, Growth and the Valuation
of Shares,” Journal of Business 34 (1961), 411–433; F. Modigliani and M. H.
Miller, “The Cost of Capital, Corporation Finance and the Theory of
Investment,” American Economic Review 48 (1958), 261–297.
22. Ibid.
23. Ibid.
Market Risk
any of the basic concepts used in risk management have evolved
from models and methodologies that were originally developed decades
ago. Nowadays, most financial organizations have established sophisticated risk management infrastructures, policies, and processes, which
support senior management in the steering and fine-tuning of the risk appetite and risk capacity of institutions. However, crises and accidents have
happened in the past and will happen again in the future. Regulators have
established rules and methods to measure the risks of individual institutions and to force them to support these risks with capital. Many quantitative models and methodologies have evolved from modern portfolio
theory, option pricing theories, and other investment-oriented methodologies. The models have been refined for different instruments and asset
types, for short and long investment horizons, etc. But the mapping of
regulatory-oriented policies onto academic models and practical everyday applications is not without problems.
This chapter analyzes the different models and approaches to market risk, including assumptions and conditions underlying these models
and approaches. It also discusses the tolerance and compatibility of both
the practical and regulatory approaches to market risk. We will focus on
topics such as time horizon, calculation approaches for probability, volatility and correlation, stability of assumptions, and the impact of liquidity.
Financial institutions, faced with the need to comply with far-reaching
regulations, have a natural incentive to achieve an understanding of the
details of risk models and approaches, and to reduce the regulatory re33
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quired capital. The capital saved through understanding academic and
regulatory frameworks allows organizations to invest the “exempt” capital in new and other business opportunities.
The Bank for International Settlement (BIS) defines market risk as “the risk
of losses in on- and off-balance-sheet positions arising from movements in
market prices.”1
The main factors contributing to market risk are equity, interest rate,
foreign exchange, and commodity risk. The total market risk is the aggregation of all risk factors. In addition to market risk, the price of financial
instruments may be influenced by the following residual risks: spread
risk, basis risk, specific risk, and volatility risk:
Spread risk is the potential loss due to changes in spreads between
two instruments. For example, there is a credit spread risk
between corporate and government bonds.
Basis risk is the potential loss due to pricing differences between
equivalent instruments, such as futures, bonds, and swaps.
Specific risk refers to issuer-specific risk—e.g., the risk of holding a
corporate bond versus a Treasury futures contract. How to best
manage specific risk has been extensively researched and is still a
topic of debate. According to the capital asset pricing model
(CAPM), specific risk is entirely diversifiable. (See Section 2.4.1
for a discussion of the CAPM.)
Volatility risk is defined as the potential loss due to fluctuations in
(implied) volatilities and is referred to as vega risk.
To determine the total price risk of financial instruments, market risk
and residual risk have to be aggregated. Risk is not additive. Total risk is
less than the sum of its parts, because the diversification between different
assets and risk components has to be considered (i.e., the correlation
would never be 1). This effect is described as diversification effect. High diversification effect between market and residual risk is expected due to
the low correlation.
Table 2-1 lists the key risk dimensions that give rise to market and
credit exposure.
Risk can be analyzed in many dimensions. Typically, risk dimensions are quantified as shown in Figure 2-1, which illustrates their interrelationship. Fluctuations in market rates can also give rise to counterparty
credit exposure and credit risk, as an increasing interest-rate level makes it
more difficult for the issuer to pay the accrued interest rate from the operative cash flow, and as the higher interest rates lower the profit margin.
Market Risk
T A B L E 2-1
Key Risk Dimensions Giving Rise to Market and Credit Exposure
Risk taker
Position, portfolio, trading desk, business unit
Risk factor
Equity, interest rate, foreign-exchange currency,
and commodity
Country or region
Europe, Americas, Asia Pacific
Maturity or duration
1 week, 1 month, 3 months . . . 30 years
Instrument or instrument type
Cash, options, forwards, futures
Crédit Suisse, UBS, Morgan Stanley
Counterparty trading limits should be in place to limit credit exposure
due to market-driven instruments, such as swaps and forwards. The management of credit exposure for market-driven instruments is discussed
further in Chapter 3.
Business risk is not included in the definition of risk used in this book
(see Chapter 1). Business and market risk are two key sources of risk that
can impact a company’s ability to achieve earnings or cash-flow targets
(see Figure 2-2). The relative magnitude of business risk to market risk
varies from company to company and thus reflects the approach and polF I G U R E 2-1
Key Risk Dimensions Giving Rise to Market and Credit Exposure. (Source: Modified
from RiskMetrics Group, Risk Management: A Practical Guide, New York: RiskMetrics
Group, 1999, p. 15. Copyright © 1999 by RiskMetrics Group, all rights reserved. RiskMetrics is a registered trademark of RiskMetrics Group, Inc., in the United States and in
other countries. Reproduced with permission of RiskMetrics Group, LLC.)
Risk Taker
Operational Risk
Market Risk
Risk Taker
i sk
it R
Market Risk
Risk Factor
Risk Factor
Credit Risk
F I G U R E 2-2
Differentiation Between Market Risk and Business Risk. (Source: Modified from RiskMetrics Group, CorporateMetrics—Technical Document, New York: RiskMetrics Group,
1999, p. 5, chart 1. Copyright © 1999 by RiskMetrics Group, all rights reserved.
CorporateMetrics is a registered trademark of RiskMetrics Group, Inc., in the United
States and in other countries. Reproduced with permission of RiskMetrics Group, LLC.)
Product placement
Interest rate
Data quality
icy for managing both types of risks; it also helps set the tone for a company’s risk management culture and awareness. When discussing business
risk, we are referring to the uncertainty (positive and negative) related to
the business decisions that companies make and to the business environment in which companies operate. For example, business risk can arise
from investment decisions and strategy, product development choices,
marketing approaches, product placement issues, and client behavior uncertainty. Broadly speaking, these are decisions with an inherent long-term
horizon and involve structural risks that companies are “paid to take” in
order to generate profits. Companies evaluate and take business risks in
areas based on their expertise and, to varying degrees, with significant influence over potential returns. In contrast, market risk refers to the uncertainty of future financial results that arises from market-rate changes.
Market risk can impact on a company’s business in many different
ways. For example, operating margins can be eroded due to the rising
prices of raw materials or depreciating currencies in countries in which a
company has foreign sales (direct market risk impact). Changes in the market environment may eventually force companies to adjust the prices of
their products or services, potentially altering sales volumes or competitiveness, depending on the positioning and market exposures of the company’s competitors (the indirect impact of market risk on business results).
Some organizations may be “paid” to take market risks (e.g., financial organizations), but most seek to manage the impact of market risk on financial results (this is especially true of most nonfinancial organizations).
Financial organizations have overlapping business and market risks.
However, as their “raw materials” are currencies, interest rates, etc., fi-
Market Risk
nancial organizations have to keep business and market risks separated to
realize success from intended business strategies and decisions, and from
the risk-return relationship of these decisions.
Investment diversification was a well-established practice long before
Markowitz published his paper on portfolio selection in 1952.2 The development of the modern portfolio theory and of option pricing theories had
its roots some decades before Markowitz. These mostly quantitative approaches were not the first to provide diversification for their customers,
because such approaches were modeled on the investment trusts of Scotland and England, which began in the middle of the nineteenth century,
and diversification had occurred even earlier. In The Merchant of Venice,
Shakespeare has the merchant Antonio say:
My ventures are not in one bottom trusted,
Nor to one place; Nor is my whole estate
Upon the fortune of this present year;
Therefore, my merchandise makes me not sad.3
Prior to Markowitz’s 1952 article, there was no adequate quantitative theory of investment established that covered the effects of diversification when risks are correlated, distinguished between efficient and
inefficient portfolios, and analyzed risk–return trade-offs on the portfolio
as a whole. In order to understand the benefits and pitfalls of the theories
and models currently used for regulatory and management purposes, it is
necessary to understand the development of portfolio theory. In 1935,
Hicks discussed the need for an improved theory of money and the desirability of building a theory of money along the same lines as the already
existing theory of value.4 Hicks introduced risk into his analysis. Specifically, he noted: “The risk-factor comes into our problem in two ways: First,
as affecting the expected period of investment, and second, as affecting
the expected net yield of investment.”5 Hicks represents the probabilities
of risk dispersions by a mean value and by some appropriate measure of
dispersion. Hicks was a forerunner of Tobin6 in seeking to explain the demand for money as a consequence of the investor’s desire for low risk as
well as high return. Beyond that, there is little similarity between the two
authors. Hicks, unlike Tobin or the appendix in Hicks7 (1962), did not designate standard deviation or any other specific measure of dispersion as
representing risk for the purposes of analysis. Hicks could not demonstrate a formula relating risk on the portfolio to risk on individual assets.
Hicks did not distinguish between efficient and inefficient portfolios,
lacked a coherent image of an efficient frontier, and gave no hint of any
kind of theorem explaining that all efficient portfolios that include cash
have the same allocation of distribution among risky assets.
Hicks’s article on liquidity (1962) is more precise about the formulation of risk by mentioning the standard deviation as a measure of “certainty” and the mean.8 The formalization was spelled out in a mathematical
appendix to Hicks (1962) titled “The Pure Theory of Portfolio Investment”
and in a footnote on page 796 of the work that presents a µσ-efficient set diagram. The appendix presents a mathematical model that is almost identical to Tobin’s, but with no reference to Tobin’s work. The difference between
the Hicks and Tobin models is that Hicks assumed that all correlations are
zero, whereas Tobin permitted any nonsingular covariance matrix. Specifically, Hicks presented the general formula for portfolio variance, written in
terms of correlations rather than covariances. Hicks (1962) derived the
Tobin conclusion that among portfolios which include cash, there is a linear
relationship between portfolio mean and standard deviation, and that the
proportions among risky assets remain constant along this linear portion of
the efficient frontier. Hicks presented what later was called the Tobin separation theorem.
Marschak (1938) was clearer in formulating risk by constructing an
ordinal theory of choice under uncertainty.9 He assumed a preference
ordering in the space of parameters of probability distributions—in the
simplest form—expressed by the mean and the variance. From this formulation to the analysis of portfolio selection in general is the shortest of
steps, but one not fully taken by Marschak,10 though he made tentative
moves in this direction, expressing preferences for investments by indifference curves in the mean-variance space. Marschak’s 1938 work is a
landmark on the road to a theory of markets whose participants act under
risk and uncertainty, as later developed in Tobin11 and the CAPMs.12 It is
the most significant advance of economic theory regarding risk and uncertainty prior to the publication of von Neumann and Morgenstern in
1944.13 The asset allocation decision had not been adequately addressed
by neoclassical economists at the time of Marschak. The methodology of
deterministic calculus is adequate for the decision of maximizing a consumer’s utility subject to a budget constraint (as part of the neoclassic approach), whereas portfolio selection involves making a decision amidst
uncertainty. Under these circumstances, the probabilistic notions of expected return and risk become very important.
In 1938, Williams highlighted the importance of diversification.14 He
concluded that probabilities should be assigned to possible values of a security and the mean of these values used as the value of that security. He
also concluded that by investing in many securities, risk could be virtually
eliminated. This presumption, that the law of large numbers applies to a
portfolio of securities, cannot be accepted. The returns from securities are
too intercorrelated. Diversification cannot eliminate all variance. Williams
Market Risk
suggested that the way to find the value of a risky security has always
been to add a “premium for risk” to the pure interest rate, and then use the
sum as the interest rate for discounting future receipts. Williams discussed
the separation of specific and systematic risk, without giving a clear overall framework. It should be noted, however, that Williams’s “dividend discount model” remains one of the standard ways to estimate the security
means needed for a mean-variance analysis.15
Leavens’ 1945 article on the diversification of investments concluded
that each security is acted upon by independent causes.16 Leavens made
the assumptions behind the systemic/specific risk separation very clear,
without directly tying his findings to a theoretical formulation.
On the basis of his path-breaking 1952 article, Markowitz became the
father of modern portfolio theory (MPT).17 At the same time, Roy (1952)
published an article on the same topic with similar conclusions and a clear
theoretical framework.18 The 1952 article on portfolio selection by
Markowitz proposed expected (mean) return, and variance of return, of
the portfolio as a whole as criteria for portfolio selection, both as a possible hypothesis about actual behavior and as a maxim for how investors
ought to act. The article assumed that beliefs or projections about securities
follow the same probability rules that random variables obey. From this
assumption, Markowitz concluded that the expected return on the portfolio is a weighted average of the expected returns on individual securities
and that the variance of return on the portfolio is a particular function of
the variances of, and the covariances between, securities and their weights
in the portfolio. Markowitz distinguished between efficient and inefficient
portfolios. Subsequently, this frontier became the “efficient frontier” for
what Markowitz referred to as the set of mean-variance efficient combinations. Markowitz proposed that means, variances, and covariances of securities be estimated by a combination of statistical analyses. From these
estimates, the set of mean-variance efficient combinations can be derived
and presented to the investor, who can choose the desired risk-return
combination. Markowitz used geometrical analyses of various security examples to illustrate properties of efficient sets, assuming nonnegative investments subject to a budget constraint. He showed in his 1952 article
that the set of efficient portfolios is piecewise linear (made up of connected straight lines) and the set of efficient mean-variance combinations
is piecewise parabolic.
Roy (1952) similarly proposed making choices on the basis of mean
and variance of the portfolio as a whole. Specifically, he proposed choosing the positions that maximize the portfolio’s utility, based on the return, with σ as the standard deviation of return. Roy’s formula for the
variance of the portfolio included the covariances of returns among securities. The main differences between the Roy and Markowitz approaches
were that Markowitz required nonnegative investments, whereas Roy allowed the amount invested in any security to be positive or negative.
Furthermore, Markowitz proposed allowing the investor to choose a desired portfolio from the efficient frontier, whereas Roy recommended
choosing a specific portfolio. Roy’s 1952 article was his first and last article in finance. He made this one tremendous contribution and then disappeared from the field, whereas Markowitz wrote several books and
many articles on the portfolio-selection problem and enhancements of
his 1952 article.19
The conceptual approach to market risk is closely linked historically
to the development of modern portfolio theory and the option pricing
theory. Modern portfolio theory started with the path-breaking theory of
Markowitz.20 Markowitz was the first finance theorist who explicitly included risk in portfolio analysis. The Markowitz approach is based on the
assumption of a relation between risk and return and considers the effect
of diversification, using the standard deviation or variance as a measure
for risk.
σ 2p = 冱 X 2i σ 21 + 冱 冱 XiXjρijσiσj
i=1 j=1
The portfolio return is the weighted return of the individual positions, and the portfolio risk is the weighted risk of all individual assets
and the covariance between those assets:
R p = 冱 Xiri
σ = 冱 X 2i σ 21 + 冱 冱 XiXjσij
i=1 j=1
The covariance can be expressed as a correlation term as follows:
σij = ρijσiσj
The risk-adjusted portfolio return is:
rp − rf
The efficient frontier is an outcome of Markowitz’s theory, a borderline of all portfolios with optimal risk–return relations (Figure 2-3). His ap-
Market Risk
F I G U R E 2-3
Efficient Frontier Curve and Capital Market Line.
Efficient frontier
Risk σp
proach was developed further by Tobin.21 Tobin improved the correlation
between the assets and the risk aversion by including a risk-free position.
Through combining the portfolios on the efficient frontier of Markowitz
and a risk-free position, Sharpe further developed the conceptual modeling of market risks and introduced the capital market line as the tangent
from the risk-free asset to the efficient frontier.
The Capital Asset Pricing Model
The complexity of Markowitz’s portfolio model and some generalization
of assumptions led to further developments. The capital asset pricing
model (CAPM) was developed by Sharpe,22 Lintner,23 and Mossin,24 and
later was enhanced by Black. It is a logical extension of the ideas behind
modern portfolio theory as first outlined by Markowitz. Because the
Markowitz approach makes no statement about the pricing of equities, the
CAPM offers a statement on the relevant investment risks and the risk–
return relation under the condition that the markets are in equilibrium.
The CAPM is an equilibrium model for the capital market.
The CAPM is based on the following nine assumptions:25
Utility maximization. Investors try to maximize their own
utilities; they are risk-averse.
Decision basis. Investors make their decisions only on the basis
of risk and return.
Expectations. Investors have homogeneous expectations
regarding return and risk (variance and covariance) of the assets.
One-period time horizon. Investors have identical time horizons of
one period.
Information efficiency. Information is free and simultaneously
available to all market participants.
Risk-free asset. Investors can borrow or invest in an unlimited
amount of risk-free assets.
Markets without friction. No taxes, transaction fees, restrictions
on short positions or other market restrictions exist.
Capital market equilibrium. The sum of all instruments is given
and in possession of the investors. All instruments are
marketable, and the assets are divisible to any degree. Supply
and demand are not influenced by anything other than price.
Distribution. The CAPM, like the Markowitz approach, is based
on the normal distribution of returns or a quadratic utility
All combinations are on the line between a risk-free investment and
the uncertain investment of the efficient frontier. The part between rf and
D is called the capital market line (CML) and contains only one efficient
portfolio, which is at the tangential point between the efficient frontier
and the capital market line (see Figure 2-3).
It is not enough to know the return distribution (variance) of a position; the return must be viewed relative to the market and risk components. The CAPM assumes that a certain portion of the risk of a position is
a reflection of the overall market risk, which is carried by all positions in
the market and thus cannot be diversified. This part of the risk is defined
as systematic risk, which cannot be eliminated through diversification. This
risk premium is defined as the market risk premium. In contrast, the specific risk (or unsystematic risk) cannot be explained by market events and
has its origins in position-specific factors (e.g., management errors and
competitive disadvantages). This component can be diversified and is not
rewarded by a premium.
The expected return of a specific stock is calculated as follows:
E (ri) = rf + βi ⋅ [E(rm) − rf] + εi
Market Risk
where ri = return of security i
rf = return of the risk-free asset
rm = return of the market
βi = sensitivity of security i relative to market movement m
εi = error term
2.4.2 The Security Market Line
One of the key elements of modern portfolio theory is that, despite diversification, some risk still exists. The sensitivity of a specific position relative to the market is expressed by βi (see Figure 2-4). The CAPM defines βi
as the relation of the systematic risk of a security i to the overall risk of the
F I G U R E 2-4
Security Market Line.
Expected return
et l
Risk free investment
Investment in market
covariance (rm , ri)
systematic risk of title i
βi = ᎏ ᎏ = ᎏᎏᎏ
risk of market portfolios
variance (rm)
βi = cov (ri, rm)
where ri = return of security i
rf = return of the risk-free asset
rm = return of the market
βi = sensitivity of security i relative to market movement m
εi = error term
The one-factor model is a strong simplification of the Markowitz
model, and the CAPM is a theory. The main criticisms of the CAPM are as
The market efficiency is not given in its strong form, as
not all information is reflected in the market. This
presents an opportunity for arbitrage profits, which can
be generated as long as insider information is not available
to the public.
The normal distribution is a generalization, which distorts the
results, especially for idiosyncratic risks.
The main message of market efficiency as it pertains to capital market models is that a market is considered efficient if all available data and
information are reflected in the pricing and in the demand-and-supply relation.26 Fama distinguishes three types of market efficiency: weak, semistrong, and strong.27
In a study on Swiss equities, Zimmermann and Vock28 came to the
conclusion that the test statistics (the standardized third and fourth
moment as a measure for the skewness and kurtosis, the standardized
span or studentized range, and the test from Kolmogorov-Smirnov)
point to a leptokurtic return distribution (see Figure 2-5). The study
concluded that the normal distribution has to be questioned from a
statistical point of view. The deviations are empirically marginal. The
leptokurtosis has been confirmed for U.S. equities in studies by
Fama,29 Kon,30 Westerfield,31 and Wasserfallen and Zimmermann32 (see
Figure 2-5). Zimmermann33 concluded that over a longer time horizon
(1927 to 1987), the normal distribution fits the return distribution of
Swiss equities.
Market Risk
F I G U R E 2-5
Probability %
Normal and Leptokurtic Distribution of Equity Returns.
Leptokurtotic distribution
2.4.3 Modified Form of CAPM
by Black, Jensen, and Scholes
Black, Jensen, and Scholes conducted an empirical examination of the
CAPM in 1972. They used a model without a risk-free interest rate, because
the existence of a risk-free interest rate was controversial.34 In the model
without a risk-free return, the security market line (SML) is no longer defined by the risk-free return and the market portfolio; instead, it is a multitude of combinations, as there is a multitude of zero-beta portfolios.35
The return that they were able to explain was significantly higher
than the average risk-free return within the observation period. They concluded that the model is compatible with the standard form of the CAPM,
but differentiates between borrowing and lending. The study supports the
practical observation that borrowing is more expensive than lending
money. Empirical studies support the development of the capital market
line with two interest rates, one for borrowing and one for lending money.
It is an important improvement, as it excludes the assumption that borrowing and lending are based on the same risk-free rate.36 Figure 2-6 is
based on the following equations:
E(ri) = rL + βi ⋅ [E(rm) − rL] + εi
E(ri) = rB + βi ⋅ [E(rm) − rB] + εi
F I G U R E 2-6
Efficient Frontier with Different Interest Rates for Borrowing and Lending Capital.
Efficient frontier
Risk σp
2.4.4 Arbitrage Pricing Theory
Empirical examinations of the CAPM showed significant deficiencies in
its ability to forecast and alleviate risk. These studies led to the development of the arbitrage pricing theory (APT), first introduced by Ross37 and
further developed by other scientists.
APT is based on the empirical observation that different instruments
have simultaneous and homogeneous development ranges. The theory
implicitly assumes that the returns are linked to a certain number of factors which influence the instrument prices. The part explained by these
factors is assigned to the systematic factors, whereas the nonexplainable
part of the return (and thus the risk) is assigned to specific factors.
In theory, the factors are uncorrelated, as empirical examination supports correlated factors. Such correlated factors have to be transformed
into an observation-equivalent model with uncorrelated factors. The factors cannot be observed and have to be examined empirically.
A critical difference between CAPM and APT is that APT is an equilibrium theory, based on the arbitrage condition. As long as it is possible
with intensive research to find factors that systematically impact the return
of a position, it is possible to do arbitrage based on this superior knowledge.
Market Risk
Approaches to Option Pricing
Modern portfolio theory is not based solely on return calculations. Risk and
risk management become increasingly important. As the portfolio theory
shows, despite diversification, an investor is still exposed to systematic risk.
With the development of portfolio and position insurance, an approach has
been created to hedge (insure) against unwanted moves of the underlying
position. The theoretical framework introduced a range of applications,
such as replication of indices, dynamic insurance, leveraging, immunization, structured products, etc. To understand the current state of option pricing, the different approaches, and the critics, it is necessary to summarize
the development of, and approaches to, modern option-valuation theory.
Valuation and pricing of income streams is one of the central problems of finance. The issue seems straightforward conceptually, as it
amounts to identifying the amount and the timing of the cash flows expected from holding the claims and then discounting them back to the
present. Valuation of a European-style call option requires that the mean of
the call option’s payout distribution on the expiration date be estimated,
and the discount rate be applied to the option’s expected terminal payout.
The first documented attempt to value a call option occurred near
the turn of the twentieth century. Bachelier wrote in his 1900 thesis that the
call option can be valued under the assumption that the underlying claim
follows an arithmetic Brownian motion.38 Sprenkle and Samuelson used a
geometric Brownian motion in their attempt to value options.39 As the underlying asset prices have multiplicative, rather than additive (as with the
arithmetic motion) fluctuations, the asset price distribution at the expiration date is lognormal, rather then normal. Sprenkle and Samuelson’s research set the stage, but there was still a problem. Specifically, for
implementation of their approach, the risk-adjusted rates of price appreciation for both the asset and the option are required. Precise estimation was
the problem, which was made more difficult as the option’s return depends on the asset’s return, and the passage of time.
The breakthrough came in 1973 with Black, Scholes, and Merton.40
They showed that as long as a risk-free hedge may be formed between the
option and its underlying asset, the value of an option relative to the asset
will be the same for all investors, regardless of their risk preferences. The
argument of the risk-free hedge is convincing, because in equilibrium, no
arbitrage opportunities can exist, and any arbitrage opportunity is obvious for all market participants and will be eliminated. If the observed
price of the call is above (or below) its theoretical price, risk-free arbitrage
profits are possible by selling the call and buying (or selling) a portfolio
consisting of a long position in a half unit of the asset, and a short position
in the other half in risk-free bonds. In equilibrium, no arbitrage opportunities can exist, and any arbitrage opportunity can exist.
48 Analytical Formulas
The option valuation theory goes beyond the mathematical part of the formula. The economic insight is that if a risk-free hedge between the option
and its underlying asset my be formed, risk-neutral valuation may be applied. The Black-Scholes model follows the work of Sprenkle and Samuelson. In a risk-neutral market, all assets (and options) have an expected rate
of return equal to the risk-free interest rate. Not all assets have the same
expected rate of price appreciation. Some assets, such as bonds, have
coupons, and equities have dividends. If the asset’s income is modeled as
a constant and continuous proportion of the asset price, the expected rate
of price appreciation on the asset equals the interest rate less the cash disbursement rate. The Black-Scholes formula covers a wide range of underlying assets. The distinction between the valuation problems described as
follows rests in the asset’s risk-neutral price appreciation parameter:
Non-dividend-paying stock options. The best-known option
valuation problem is that of valuing options on non-dividendpaying stocks. This is, in fact, the valuation problem addressed by
Black and Scholes in 1973.41 With no dividends paid on the
underlying stock, the expected price appreciation rate of the stock
equals the risk-free rate of interest, and the call option valuation
equation becomes the familiar Black-Scholes formula.
Constant-dividend-yield stock options. Merton generalized stock
option valuation in 1973 by assuming that stocks pay dividends
at a constant, continuous dividend yield.42
Futures options. Black valued options on futures in 1976.43 In a
risk-neutral world with constant interest rates, the expected rate
of price appreciation on a futures contract is zero, because it
involves no cash outlay.
Futures-style futures options. Following the work of Black, Asay
valued futures-style futures options.44 Such options, traded on
various exchanges, have the distinguishing feature that the
option premium is not paid up front. Instead, the option position
is marked to market in the same manner as the underlying
futures contract.
Foreign currency options. Garman and Kohlhagen valued options
on foreign currency in 1983.45 The expected rate of price
appreciation of a foreign currency equals the domestic rate of
interest less the foreign interest.
Dynamic portfolio insurance. Dynamic replication is at the heart
of one of the most popular financial products of the 1980s—
dynamic portfolio insurance. Because long-term index put
options were not traded at the time, stock portfolio managers had
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to create their own insurance by dynamically rebalancing a
portfolio consisting of stocks and risk-free bonds. The weights in
the portfolio show that as stock prices rise, funds are transferred
from bonds to stocks, and vice versa.
Compound options. An important extension of the Black-Scholes
model that falls in the single underlying asset category is the
compound option valuation theory developed by Geske.46
Compound options are options on options. A call on a call, for
example, provides its holder with the right to buy a call on the
underlying asset at some future date. Geske shows that if these
options are European-style, valuation formulas can be derived.
American-style call options on dividend-paying stocks. The Geske
compound option model has been applied in other contexts. Roll,
Geske, and Whaley developed a formula for valuing an
American-style call option on a stock with known discrete
dividends.47 If a stock pays a cash dividend during the call’s life,
it may be optimal to exercise the call early, just prior to dividend
payment. An American-style call on a dividend-paying stock,
therefore, can be modeled as a compound option providing its
holder with the right, on the ex-dividend date, either to exercise
early and collect the dividend, or to leave the position open.
Chooser options. Rubinstein used the compound option
framework in 1991 to value the “chooser” or “as-you-like-it”
options traded in the over-the-counter market.48 The holder of a
chooser option has the right to decide at some future date
whether the option is a call or a put. The call and the put usually
have the same exercise price and the same time remaining to
Bear market warrants with a periodic reset. Gray and Whaley used
the compound option framework to value yet another type of
contingent claim, S&P 500 bear market warrants with a periodic
reset traded on the Chicago Board Options Exchange and the
New York Stock Exchange.49 The warrants are originally issued as
at-the-money put options but have the distinguishing feature that
if the underlying index level is above the original exercise on
some prespecified future date, the exercise price of the warrant is
reset at the then-prevailing index level. These warrants offer an
intriguing form of portfolio insurance whose floor value adjusts
automatically as the index level rises. The structure of the
valuation problem is again a compound option, and Gray and
Whaley’s 1997 paper provides the valuation formula.
Lookback options. A lookback option is another exotic that has
only one underlying source of price uncertainty. Such an option’s
exercise price is determined at the end of its life. For a call, the
exercise price is set equal to the lowest price that the asset
reached during the life of the option; for a put, the exercise price
equals the highest asset price. These buy-at-the-low and sell-atthe-high options can be valued analytically. Formulas are
provided in Goldman, Sosin, and Gatto’s 1979 paper.50
Barrier options. Barrier options are options that either cease to
exist or come into existence when some predefined asset price
barrier is hit during the option’s life. A down-and-out call, for
example, is a call that gets knocked out when the asset price falls
to some prespecified level prior to the option’s expiration.
Rubinstein and Reiner’s 1991 paper provides valuation equations
for a large family of barrier options.51 Approximation Methods
Many valuation problems do not have explicit closed-form solutions.
Probably the best-known example of this is the valuation of Americanstyle options. With American-style options, the option holder has an infinite number of exercise opportunities between the current date and the
option’s expiration date, making the problem challenging from a mathematical standpoint. Hundreds of different types of exotic options trade in
the OTC market, and many, if not most, do not have analytical formulas.
Nonetheless, they can all be valued accurately using the Black-Scholes
model. If a risk-free hedge can be formed between the option and the underlying asset, the Black-Scholes model risk-neutral valuation theory can
be applied, albeit using numerical methods. A number of numerical
methods for valuing options are lattice based. These methods replace the
Black-Scholes model assumption that asset price moves smoothly and
continuously through time with an assumption that the asset price moves
in discrete jumps over discrete intervals during the option’s life:
Binomial method. Perhaps the best-known lattice-based method is
the binomial method, developed independently in 1979 by Cox,
Ross, and Rubinstein and Rendleman and Bartter.52 In the
binomial method, the asset price jumps up or down, by a fixed
proportion, at each of a number of discrete time steps during the
option’s life. The length of each time step is determined when the
user specifies the number of time steps. The greater the number of
time steps, the more precise the method. The cost of the increased
precision, however, is computational speed. With n time steps, 2n
asset price paths over the life of the option are considered. With 20
time steps, this means more than 1 million paths.
The binomial method has wide applicability. Aside from the
American-style option feature, which is easily incorporated
Market Risk
within the framework, the binomial method can be used to value
many types of exotic options. Knockout options, for example, can
be valued using this technique. One simply imposes a different
check on the calculated option values at the nodes of the intermediate time steps between 0 and n, i.e., if the underlying asset price
falls below the option’s barrier, the option value at that node is
set equal to 0. The method can also be extended to handle multiple sources of asset price uncertainty. Boyle, Evnine, and Gibbs
adapt the binomial procedure to handle exotics with multiple
sources of uncertainty, including options on the minimum and
maximum, spread options, and so on.53
Trinomial method. The trinomial method is another popular
lattice-based method. As outlined by Boyle, this method allows
the asset to move up, move down, or stay the same at each time
increment.54 Again, the parameters of the discrete distribution are
chosen in a manner consistent with the lognormal distribution,
and the procedure begins at the end of the option’s life and works
backward. By having three branches instead of two, the trinomial
method provides greater accuracy than the binomial method for a
given number of time steps. The cost, of course, is that the greater
the number of branches, the slower the computational speed.
Finite difference method. The explicit finite difference method was
the first lattice-based procedure to be applied to option valuation.
Schwartz applied it to warrants, and Brennan and Schwartz
applied it to American-style put options on common stocks.55 The
finite difference method is similar to the trinomial method in the
sense that the asset price moves up, moves down, or stays the
same at each time step during the option’s life. The difference in
the techniques arise only from how the price increments and the
probabilities are set. In addition, finite difference methods calculate
an entire rectangle of node values rather than simply a tree.
Monte Carlo simulation. Boyle introduced Monte Carlo simulation
to option valuation.56 Like the lattice-based procedures, the
technique involves simulating possible paths that the asset price
may take over the life of the option. Again, the simulation is
performed in a manner consistent with the lognormal asset price
process. To value a European-style option, each sample run is
used to produce a terminal asset price, which, in turn, is used to
determine the terminal option value. With repeated sample runs, a
distribution of terminal options values is obtained, and the
expected terminal option value may be calculated. This expected
value is then discounted to the present to obtain the option
valuation. An advantage of the Monte Carlo method is that the
degree of valuation error can be assessed directly, using the
standard error of the estimate. The standard error equals the
standard deviation of the terminal option values divided by the
square root of the number of trials. Another advantage of the
Monte Carlo technique is its flexibility. Because the path of the
asset price beginning at time 0 and continuing throughout the life
of the option is observed, the technique is well suited for handling
barrier-style options, Asian-style options, Bermuda-style options,
and the like. Moreover, it can easily be adapted to handle multiple
sources of price uncertainty. The technique’s chief disadvantage is
that it can be applied only when the option payout does not
depend on its value at future points in time. This eliminates the
possibility of applying the technique to American-style option
valuation, in which the decision to exercise early depends on the
value of the option that will be forfeit.
Compound option approximation. The quasi-analytical methods
for option valuation are quite different from the procedures that
attempt to describe asset price paths. Geske and Johnson, for
example, use a Geske compound option model to develop an
approximate value for an American-style option.57 The approach
is intuitively appealing. An American-style option, after all, is a
compound option with an infinite number of early exercise
opportunities. While valuing an option in this way makes
intuitive sense, the problem is intractable from a computational
standpoint. The Geske-Johnson insight is that although we
cannot value an option with an infinite number of early exercise
opportunities, we can extrapolate its value by valuing a sequence
of “pseudo-American” options with zero, one, two, and perhaps
more early exercise opportunities at discrete, equally spaced
intervals during the option’s life. The advantage that this offers is
that each of these options can be valued analytically. With each
new option added to the sequence, however, the valuation of a
higher-order multivariate normal integral is required. With no
early exercise opportunities, only a univariate function is
required. However, with one early exercise opportunity, a
bivariate function is required; with two opportunities, a trivariate
function is required, and so on. The more of these options used in
the series, the greater the precision in approximating the limiting
value of the sequence. The cost of increased precision is that
higher-order multivariate integral valuations are time-consuming
Quadratic approximation. Barone-Adesi and Whaley presented a
quadratic approximation in 1987.58 Their approach, based on the
Market Risk
work of MacMillan, separates the value of an American-style
option into two components: the European-style option value and
an early exercise premium.59 Because the Black-Scholes model
formula provides the value of the European-style option, they
focus on approximating the value of the early exercise premium.
By imposing a subtle change on the Black-Scholes model partial
differential equation, they obtain an analytical expression for the
early exercise premium, which they then add to the Europeanstyle option value, thereby providing an approximation of the
American-style option value. The advantages of the quadratic
approximation method are speed and accuracy. Generalizations
The generalizations of the Black-Scholes option valuation theory focus on
the assumed asset price dynamics. Some examine the valuation implications of modeling the local volatility rate as a deterministic function of the
asset price or time or both. Others examine the valuation implications
when volatility, like asset price, is stochastic.
Under the assumption that the local volatility rate is a deterministic
function of time or the asset price or both, the Black-Scholes model riskfree hedge mechanisms are preserved, so risk-neutral valuation remains
possible. The simplest in this class of models is the case in which the local
volatility rate is a deterministic function of time. For this case, Merton
showed that the valuation equation for a European-style call option is the
Black-Scholes model formula, where the volatility parameter is the average local volatility rate over the life of the option.60
Other models focus on the relationship between asset price and
volatility and attempt to account for the empirical fact that, in at least
some markets, volatility varies inversely with the level of asset price. One
such model is the constant elasticity of variance model proposed by Cox
and Ross.61 However, valuation can be handled straightforwardly using
lattice-based or Monte Carlo simulation procedures.
Derman and Kani, Dupire, and Rubinstein and Reiner recently developed a valuation framework in which the local volatility rate is a deterministic (but unspecified) function of asset price and time.62 If the
specification of the volatility function is known, any of the lattice-based or
simulation procedures can be applied to option valuation. Unfortunately,
the structural form is not known. To circumvent this problem, these authors parameterize their model by searching for a binomial or trinomial
lattice that achieves an exact cross-sectional fit of reported option prices.
An exact cross-sectional fit is always possible, because there are as many
degrees of freedom in defining the lattice (and, hence, the local volatilityrate function) as there are option prices. With the structure of the implied
tree identified, it becomes possible to value other, more exotic, OTC options and to refine hedge ratio computations.
The effects of stochastic volatility on option valuation are modeled
by either superimposing jumps on the asset price process or allowing
volatility to have its own diffusion process or both. Unfortunately, the introduction of stochastic volatility negates the Black-Scholes model riskfree hedge argument, because volatility movements cannot be hedged. An
exception to this rule is provided by Merton, who adds a jump term to the
usual geometric Brownian motion governing asset price dynamics.63 By
assuming that the jump component of an asset’s return is unsystematic,
the Merton model can create a risk-free portfolio in the Black-Scholes
model sense and apply risk-neutral valuation. Indeed, Merton finds analytical valuation formulas for European-style options. If the jump risk is
systematic, however, the Black-Scholes model risk-free hedge cannot be
formed, and option valuation will be utility-dependent.
A number of authors model asset price and asset price volatility as
separate, but correlated, diffusion processes. Asset price is usually assumed to follow geometric Brownian motion. The assumptions governing
volatility vary. Hull and White, for example, assume that volatility follows
geometric Brownian motion.64 Scott models volatility using a meanreverting process, and Wiggins uses a general Wiener process.65 Bates
combines both jump and volatility diffusions in valuing foreign currency
options. Except in the uninteresting case in which asset price and volatility movements are independent, these models require the estimation of
risk premiums.66 The problem when volatility is stochastic is that a riskfree hedge cannot be created, because volatility is not a traded asset. But
perhaps this problem is only temporary. The critical issue for all options,
of course, is correct contract design.
Alan Greenspan has made it very clear that the assumptions and conditions must be fully discussed and understood when applying quantitative
models such as value at risk (VaR):
Probability distributions estimated largely, or exclusively, over cycles that
do not include periods of panic will underestimate the likelihood of extreme
price movements because they fail to capture a secondary peak at the extreme negative tail that reflects the probability of occurrence of a panic. Furthermore, joint distributions estimated over periods that do not include
panics will underestimate correlations between asset returns during panics.
Under these circumstances, fear and disengagement on the part of investors
holdings net long positions often lead to simultaneously declines in the values of private obligations, as investors no longer realistically differentiate
Market Risk
among degrees of risk and liquidity, and to increase in the values of riskless
government securities. Consequently, the benefits of portfolio diversification will tend to be overestimated when the rare panic periods are not taken
into account.67
The 1988 Basel accord provided the first step toward tighter risk
management and enforceable international regulation with similar structural conditions for financial supervision.68 The Basel accord set minimum
capital requirements that must be met by banks to guard against credit
risk. This agreement led to a still-evolving framework to impose capital
adequacy requirements to guard against market risks.
The reasoning behind regulation is multilayered and complex. One
could ask why regulations are necessary. In a free market, investors should
be free to invest in firms that they believe to be profitable, and as owners of
an institution, they should be free to define the risk profile within which
the institution should be free to act and evolve. Essentially, this is what
happened to Barings, where complacent shareholders failed to monitor the
firm’s management (see Section 6.6). Poor control over traders led to increasingly risky activities and, ultimately, bankruptcy. In freely functioning
capital markets, badly managed institutions should be allowed to fail. Such
failures also serve as powerful object lessons in risk management.
Nevertheless, supervision is generally viewed as necessary when
free markets appear to be unable, themselves, to allocate resources efficiently. For financial institutions, this is the rationale behind regulations to
protect against systemic risk (externalities) and to protect client assets (i.e.,
deposit insurance).
Systemic risk arises when an institution’s failure affects other participants in the market. Here the fear is that a default by one institution will
have a cascading effect on other institutions, thus threatening to destabilize the entire financial system. Systemic risk is rather difficult to evaluate,
because it involves situations of extreme instability, which happen infrequently. In addition, regulators tend to take preventive measures to protect the system before real systemic damage is caused.69
Deposit insurance also provides a rationale for regulative measures.
By nature, bank deposits have destabilizing potential. Depositors are
promised that the full face value of their investments will be repaid on demand. If customers fear that a bank’s assets have fallen behind its liabilities, they may then rationally trigger a run on the bank. Given that banks
invest in illiquid assets, including securities and real estate, the demand
for repayment will force liquidation at great cost.
One solution to this problem is government guarantees on bank deposits, which reduce the risk of bank runs. These guarantees are also
viewed as necessary to protect small depositors who have limited financial experience and cannot efficiently monitor their banks.
There is an ongoing argument that deposit insurance could be provided by the private sector instead of the government. Realistically, however, private financial organizations may not be able to provide financial
transfers to investors if large macroeconomic shocks or sector collapses
occur, such as the U.S. savings and loan crisis of the 1980s. On the other
hand, applying Darwinism to capital markets, it should be possible to
eliminate failing institutions from the market and replace them with fitter
This government guarantee is no “panacea, for it creates a host of
other problems, generally described under the rubric of moral hazard (see
Section 1.4). Given government guarantees, there is even less incentive for
depositors to monitor their banks. As long as the cost of the deposit insurance is not related to the risk-profile of the activities, there will be perverse
incentives to take additional risks. The moral hazard problem, due to deposit insurance, is a rationale behind regulatory attempts to supervise
risk-taking activities. This is achieved by regulating the bank’s minimum
levels of capital, providing a reserve for failures of the institution or systemic risks. Capital adequacy requirements can also serve as a deterrent to
unusual risk taking if the amount of capital set aside is tied to the amount
of risk undertaken.
Alan Greenspan stated in 1999 that the current regulatory standards
had been misused due to inconsistent and arbitrary treatment:
The current international standards for bank capital had encouraged bank
transactions that reduce regulatory requirements more than they reduce a
bank’s risk position. The fundamental credibility of regulatory capital standards as a tool for prudential oversight and prompt corrective action at the
largest banking organizations has been seriously undermined.71
Development of an International Framework
for Risk Regulation
The Basel Committee on Banking Supervision was founded in 1975; it is the
driving force for harmonization of banking supervision regulation on an international level, and it substantially supports cross-border enforcement of
cooperation among national regulators. The committee’s recommendations
have no internal binding power, but based on the material power of persuasion and the implementation of its recommendations at the local level by
the members of the Committee, it has a worldwide impact.72
Capital adequacy is the primary focus of the committee, as capital
calculation has a central role in all local regulations, and the standards of
the BIS are broadly implemented. The standards are intended to
strengthen the international finance system and reduce the distortion of
normal trading conditions by arbitrary national requirements. The BIS
Market Risk
recommendations apply only to international banks and consolidated
banking groups. They are minimum standards, allowing local regulators
to set or introduce higher requirements. The Basel Committee intends to
develop and enhance an international regulatory network to increase the
quality of banking supervision worldwide.
Framework of the 1988 BIS Capital
Adequacy Calculation
Since its inception, the Basel Committee has been very active on the issue
of capital adequacy. A landmark financial agreement was reached with
the Basel accord, concluded on July 15, 1988, by the central bankers of
the G-10 countries.73 The regulators announced that the accord would result in international convergence of supervisory regulations governing
the capital adequacy of international banks. Though minimal, these capital adequacy standards increase the quality and stability of the international banking system, and thus help to reduce distortion between
international banks. The main purpose of the 1988 Basel accord was to
provide general terms and conditions for commercial banks by means of
a minimum standard of capital requirements to be applied in all member
countries. The accord contained minimal capital standards for the support
of credit risks in balance and off-balance positions, as well as a definition
of the countable equity capital. The Basel capital accord was modified in
1994 and 1995 with regard to derivatives instruments and recognition of
bilateral netting agreements.74
With the Cooke defined ratio, the 1988 accord created a common
measure of solvency. However, it covers only credit risks and thus deals
solely with the identity of banks’ debtors. The new ratios became binding
by regulation in 1993, covering all insured banks of the signatory countries. The Cooke Ratio
The Basel accord requires that banks hold capital equal to at least 8 percent
of their total risk-weighted assets. Capital, however, is interpreted more
broadly than the usual definition of equity, because its goal is to protect
deposits. It consists of two components:
Tier 1 capital. Tier 1 capital, or core capital, includes stock issues
and disclosed reserves. General loan loss reserves constitute
capital that has been dedicated to funds to absorb potential future
losses. Real losses in the future are funded from the reserve
account rather than through limitation of earnings, smoothing
out income over time.
Tier 2 capital. Tier 2 capital, or supplementary capital, includes
perpetual securities, undisclosed reserves, subordinated debt
with maturity longer than five years, and shares redeemable at
the option of the issuer. Because long-term debt has a junior
status relative to deposits, debt acts as a buffer to protect
depositors (and the deposit insurer).
The Cooke ratio requires an 8 percent capital charge, at least 50 percent of which must be covered by Tier 1 capital. The general 8 percent capital charge is multiplied by risk capital weights according to predetermined
asset classes. Government bonds, such as Treasuries, Bundesobligationen,
Eidgenossen, and so forth are obligations allocated to the Organization for
Economic Cooperation and Development (OECD) government papers,
which have a risk weight of zero. In the same class fall cash and gold held
by banks. As the perceived credit risk increases (nominally), so does the
risk weight. Other asset classes, such as claims on corporations (including
loans, bonds, and equities), receive a 100 percent weight, resulting in the
required coverage of 8 percent of capital.
Signatories of the Basel accord are free to impose higher local capital
requirements in their home countries.75 For example, under the newly established bank capital requirements, U.S. regulators have added a capital
restriction which requires that Tier 1 capital must comprise no less than 3
percent of total assets. Activity Restrictions
In addition to the weights for the capital adequacy calculation, the Basel
accord set limits on excessive risk taking. These restrictions relate to large
risks, defined as positions exceeding 10 percent of the bank’s capital.
Large risks must be reported to regulatory authorities on a formal basis.
Positions exceeding 25 percent of the bank’s capital are not allowed (unless a bank has the approval of the local regulator). The sum of all largerisk exposures may not exceed 800 percent of the capital.
Criticisms of the 1988 Approach
The 1988 Basel accord had several drawbacks, which became obvious
with implementation. The main criticisms were the lack of accommodation of the portfolio approach, the lack of netting possibilities, and the way
in which market risks were incorporated.
The portfolio approach was not accommodated. Thus, correlations
between different positions of the bank’s portfolio did not
account for the portfolio risk of the bank’s activities. The Basel
accord increased the capital requirements resulting from hedging
strategies, as offsetting hedging positions were not allowed.
Netting was not allowed. If a bank nets corresponding lenders
and borrowers, the total net exposure may be small. If a
Market Risk
counterparty fails to fulfill its obligations, the overall loss may be
reduced, as the positions lent are matched by the positions
borrowed. Netting was an important driving force behind the
creation of swaps and time deposits. Swaps (of currencies and
interest rates) are derivatives contracts involving a series of
exchanges of payments and are contracted with explicit offset
provisions. In the event of a counterparty default, the bank is
exposed only to the net of the interest payments, not to the
notional amount.76
Exposures to market risk were vaguely regulated. According to the
1988 Basel accord, assets were recorded at book value. These
positions could deviate substantially from their current market
values. As a result, the accounting approach created a potential
situation in which an apparently healthy balance sheet with
acceptable capital (recorded at book value) hid losses in market
value. This regulatory approach concerning accounting created
problems for the trading portfolios of banks with substantial
positions in derivatives. This specific drawback convinced the
Basel Committee to move toward measuring market risk by the
value-at-risk approach and mark-to-market position booking.
Evolution of the 1996 Amendment
on Market Risks
In view of the increasing exposure to market risks in securities and derivatives trading, the Basel Committee created a substantial enhancement
of the credit-risk-oriented capital adequacy regulations through new
measurement rules and capital requirements to support market risks
throughout an institution. The committee published the results of its
work for discussion in January 1996.77 The discussion paper proposed
two alternative methods for risk measurement and capital requirements
to support market risks. The standard model approach was to be used by
small and midsized banks lacking the complex technological infrastructure and expertise needed to calculate daily market risk exposures. The
internal model approach could be used if the local regulator explicitly allowed the bank to use its own technological infrastructure and expertise
to calculate daily market risk exposures. Banks would have the opportunity to use both approaches simultaneously during a transition period.
After a certain time, banks would be expected to use only one model
across the institution.
Originally, the aim had been for a harmonized standard, which
should have balanced the terms of competition between the securities
dealers and the banks regarding capital requirements. The development
of such a regulative framework would have been supported by a joint
project between the Basel Committee and the stock exchange supervisory
authorities, for whom market risks have always been in the foreground.
The discussion with the Technical Committee of the International Organization of Securities Commission (IOSCO)—the international association
of supervisory authorities of the securities houses of the Western industrialized nations—failed, because the IOSCO members could not agree on a
common approach. Partly responsible for the failure was the fact that
IOSCO had no concrete capital adequacy standard. This would have required a substantial reworking of IOSCO’s regulations.
Based on this discussion, the Basel Committee published a first consultation paper in 1993, which included proposals for the regulatory treatment of market risks of debt and equity positions in the trading books. For
trading positions, the related derivatives instruments, and foreign currency risks from the banking books, the committee proposed a binding
standard approach for measurement and capital requirements to support
market risks. In addition, a proposal for the measurement of interest rate
risks based on the bank’s complete activity has been developed to identify
unexceptionally high interest rate risks (the so-called outlier concept). As
an alternative to the proposed standard approach for the measurement
and capital requirements to support market risks, the committee also considered the banks’ own internal models for the measurement and capital
requirements to support market risks. The modified recommendations of
the Basel Committee were published in April 1995. Simultaneously, another globally coordinated consultation procedure was carried out with
market participants and representatives from the local regulators. The
final capital adequacy accord for measurement and capital requirements
to support market risks was adopted by the committee in December 1995
and published in January 1996. The member countries had until the end of
1997 to include the modified capital adequacy regulation in their national
supervisory regulations.
Starting at the end of 1997, or earlier, if their supervisory authority so
prescribed, banks were required to measure and apply capital charges to
their market risks in addition to their credit risks.78 Market risk is defined
as “the risk of losses in on- and off-balance-sheet positions arising from
movements in market prices.” The following risks are subject to this
Risks pertaining to interest-rate-related instruments and equities
in the trading book
Foreign exchange risk and commodities risk throughout the bank
Market Risk
2.6.1 Scope and Coverage of Capital Charges
The final version of the amendment to the capital accord to incorporate
market risks regulates capital charges for interest-rate-related instruments
and equities and applies to the current market value of items in the bank’s
trading books. By trading book is meant the bank’s proprietary positions in
financial instruments (including positions in derivative products and offbalance-sheet instruments) which are intentionally held for short-term resale. The financial instruments may also be acquired by the bank with the
intention of benefiting in the short term from actual or expected differences
between their buying and selling prices, or from other price or interest-rate
variations; positions in financial instruments arising from matched principal brokering and market making; or positions taken in order to hedge
other elements of the trading book.79
Capital charges for foreign exchange risk and for commodities risk
apply to the bank’s total currency and commodity positions, subject to
some discretion to exclude structural foreign exchange positions:
For the time being, the Committee does not believe that it is necessary to
allow any de minimis exemptions from the capital requirements for market
risk, except for those for foreign exchange risk set out in paragraph 13 of A.3,
because the Capital Accord applies only to internationally active banks, and
then essentially on a consolidated basis; all of these are likely to be involved
in trading to some extent.80
Countable Capital Components
The definition of capital is based on that of the BIS, from the Amendment to
the Capital Accord to Incorporate Market Risks:
The principal form of eligible capital to cover market risks consists of
shareholders’ equity and retained earnings (tier 1 capital) and supplementary capital (tier 2 capital) as defined in the 1988 Accord. But banks
may also, at the discretion of their national authority, employ a third tier
of capital (“tier 3”), consisting of short-term subordinated debt as defined in paragraph 2 below for the sole purpose of meeting a proportion
of the capital requirements for market risks, subject to the following
conditions. . . .81
The definition of eligible regulatory capital remains the same as outlined in the 1988 accord and clarified in the October 27, 1998, press release
on instruments eligible for inclusion in Tier 1 capital. The ratio must be no
lower than 8 percent for total capital. Tier 2 capital continues to be limited
to 100 percent of Tier 1 capital.82
To clarify the impact of the amendment for market risk on the risk
steering of the banks, the capital definitions are summarized as follows:
Banks are entitled to use Tier 3 capital solely to support market
risks as defined in Parts A and B of the amendment. This means
that any capital requirement arising in respect of credit and
counterparty risk in the terms of the 1988 accord, including the
credit counterparty risk in respect of derivatives in both trading
and banking books, needs to be met by the existing definition of
capital in the 1988 accord (i.e., Tiers 1 and 2).
Tier 3 capital is limited to 250 percent of a bank’s Tier 1 capital
that is required to support market risks. This means that a
minimum of about 28.5 percent of market risks needs to be
supported by Tier 1 capital that is not required to support risks in
the remainder of the book.
Tier 2 elements may be substituted for Tier 3 up to the same limit
of 250 percent if the overall limits in the 1988 accord are not
breached. That is, eligible Tier 2 capital may not exceed total Tier
1 capital, and long-term subordinated debt may not exceed 50
percent of Tier 1 capital.
In addition, because the committee believes that Tier 3 capital is
appropriate only to meet market risk, a significant number of
member countries are in favor of retaining the principle in the
present accord that Tier 1 capital should represent at least half of
total eligible capital—that is, that the sum total of Tier 2 plus Tier
3 capital should not exceed total Tier 1. However, the committee
has decided that any decision whether to apply such a rule
should be a matter for national discretion. Some member
countries may keep the constraint, except in cases in which
banking activities are proportionately very small. In addition,
national authorities will have discretion to refuse the use of shortterm subordinated debt for individual banks or for their banking
systems generally.
For short-term subordinated debt to be eligible as Tier 3 capital, it
must, if circumstances demand, be capable of becoming part of a bank’s
permanent capital and thus be available to absorb losses in the event of insolvency. It must, therefore, at a minimum:
Be unsecured, subordinated, and fully paid up
Have an original maturity of at least two years
Not be repayable before the agreed repayment date unless the
supervisory authority agrees
Be subject to a lock-in clause which stipulates that neither interest
nor principal may be paid (even at maturity) if such payment
means that the bank will fall below or remain below its minimum
capital requirement
Market Risk
2.6.3 The de Minimis Rule
The Basel Committee has ruled out the use of simplifying approaches, allowing small institutions with negligible exposures to be excluded from
the capital requirement for market risks:
For the time being, the Committee does not believe that it is necessary to
allow any de minimis exemptions from the capital requirements for market
risk, except for those for foreign exchange risk set out in paragraph 13 of A.3,
because the Capital Accord applies only to internationally active banks, and
then essentially on a consolidated basis; all of these are likely to be involved
in trading to some extent.83
However, several countries, such as Germany and Switzerland, have included de minimis rules in their national regulations, especially with regard to asset management–oriented institutions which have negligible
market risk positions.84 Assuming the approval of the national authorities
(subject to compliance with the criteria for de minimis exception), local
supervisors are free to monitor the relevant exposures in the non–de minimis institutions more carefully. The approach is reasonable for smaller
asset management and private banking institutions, which do not take
substantial amounts of risk on their own books, as they execute on behalf
of their clients. The important distinction is between organizations subject to the standard model approach and those subject to the internal
model approach, as this difference determines how risk has to be supported by capital. Thus it fixes capital that could be used for other business purposes.85
With the standard approach, a standardized framework for a quantitative
measurement of market risks and the capital calculation to support market risks is given for all banks. The capital adequacy requirements are preset, depending on the risk factor categories:
Interest-rate and equity-price risks in the trading book
Currency, precious metals, and commodity risks in the entire
The capital adequacy requirements are calculated for each individual position and then added to the total capital requirement for the institution; see Table 2-2.
For interest-rate risk, the regulations define a set of maturity bands,
within which net positions are identified across all on- and off-balancesheet items. A duration weight is then assigned to each of the 13 bands,
varying from 0.20 percent for positions under 3 months to 12.50 percent
T A B L E 2-2
Capital Adequacy Requirements with the Standardized Measurement Method
Interest-rate-sensitive position
Risk Decomposition
General market risk: duration or
maturity method
Specific market risk: net position by
issuer × weight factor, depending on the
instrument class
Equity instruments
General market risk: 8% of the net
position per national market
Specific market risk: 8% of the net
position per issuer
Precious metals
10% of the net position
10% of all net long positions or all net
short positions, whichever is greater
20% of the net position per commodity
group + 3% of the brutto position of all
commodity groups
for positions over 20 years. The sum of all weighted net positions then
yields an overall interest-rate-risk indicator. Note that the netting of positions within a band (horizontal) and aggregation across bands (vertical)
essentially assumes perfect correlation across debt instruments.
For currency and equity risk, the market risk capital charge is essentially 8 percent of the net position; for commodities, the charge is 15 percent. All of these capital charges apply to the trading books of commercial
banks, except for currency risks, which apply to both trading and banking
The framework for measurement of market risks and the capital calculation to support market risks has to ensure that banks and securities
dealers have adequate capital to cover potential changes in value (losses)
caused by changes in the market price. Not including derivatives, which
usually exhibit nonlinear price behavior, the potential loss based on the
linear relationship between the risk factors and the financial instruments
corresponds to the product of position amount, sensitivity of the position
value regarding the relevant risk factors, and potential changes in the relevant risk factors. Equation (2.9) provides a methodological basis for the
measurement of market risks as well as the calculation of the capital requirements based on the standard approach.
Market Risk
∆w = w ⋅ s ⋅ ∆ f
where ∆w = change in value of the position
w = value of the position
s = sensitivity
∆f = change in the price-relevant factor
For the quantification of market risks using Equation (2.9), the direction of the change of the relevant risk factors is less important than the
change per se. This is based on the assumption that the long and short positions are influenced by the same risk factors, which causes a loss on the
net position. The extent of the potential changes of the relevant risk factors
has been defined by BIS such that the computed potential losses, which
would have to be supported by capital, cover approximately 99 percent of
the value changes that have been observable over the last 5 to 10 years
with an investment horizon of 2 weeks.
The framework of the standard approach is based on the buildingblock concept, which calculates interest rate and equity risks in the trading
book and currency, precious metals, and commodity risks in the entire institution separate from capital requirements, which are subsequently aggregated by simple addition. The building-block concept is also used
within the risk categories. As with equity and interest-rate risks, separate
requirements for general and specific market risk components are calculated and aggregated. From an economic viewpoint, this concept implies
that correlations between the movements—the changes in the respective
risk factors—are not included in the calculation and aggregation. With
movements in the same direction, a correlation of +1 between the risk factors is assumed, and with movements in opposite directions, a correlation
of −1 is assumed. The standard approach is thus a strong simplification of
reality, as the diversification effect based on the correlations between the
risk factors is completely neglected, which results in a conservative risk
calculation. Related to this risk measurement approach is a higher capital
requirement (relative to the internal model).
Contrary to the internal model, apart from the general requirements
for risk management in trading and for derivatives, no further specific
qualitative minimums are required. The implementation must be carefully examined by the external auditor, in compliance with the capital adequacy regulations, and the results confirmed to the national regulator.
2.7.1 General and Specific Risks for Equityand Interest-Rate-Sensitive Instruments
In the standard approach, the general and specific components of market
risk for the equity- and interest-rate-sensitive instruments in the trading
book are calculated separately. The different types of market risks can be
defined as follows:
Specific risk includes the risk that an individual debt or equity
security may move by more or less than the general market in
day-to-day trading (including periods when the whole market is
volatile) and event risk (when the price of an individual debt or
equity security moves precipitously relative to the general
market, e.g., on a takeover bid or some other shock event; such
events would also include the risk of default).86 The specific
market risk corresponds to the fraction of market risk associated
with the volatility of positions or a portfolio that can be explained
by events related to the issuer of specific instruments and not in
terms of general market factors. Price changes can thus be
explained by changes in the rating (upgrade or downgrade) of
the issuer or acquiring or merging partner.
General market risk corresponds to the fraction of market risk
associated with the volatility of positions or a portfolio that can
be explained in terms of general market factors, such as changes
in the term structure of interest rates, changes in equity index
prices, currency fluctuation, etc.
The capital adequacy requirements of the revised regulation assume
that splitting the individual risk components is possible. The credit risk
components of market risk positions may not be neglected, as they as well
are regulated and require capital support.
Forward transactions have a credit risk if a positive replacement value
(claims against the counterparties) exists. Off-balance-sheet positions
have to be converted into the credit equivalents and supported by capital.
A critical condition for the application of the current market risk
measurement regulations is the correct mapping of the positions. In order
to do so, all trading-book positions must be valued mark-to-market on a
daily basis. In an additional step, all derivatives belonging to the trading
book must be decomposed adequately to allocate the risk exposure to the
corresponding risk factors. An aggregation between spot and forward
rates requires the mapping of forwards, futures, and swaps as combinations of long and short positions, in which the forward position is mapped
as either of the following:
A long (or short) position in the underlying physical or fictive
(e.g., derivatives) basis instruments
An opposite short (or long) position in the underlying physical or
fictive (e.g., derivatives) basis instruments
An interest-rate swap can be decomposed as shown in Figure 2-7.
Market Risk
F I G U R E 2-7
Decomposition of an Interest-Rate Swap.
Interest-rate swap
(fixed receiver)
Fixed leg 6%
Floating leg 3-mo
Reset date monthly
Time to maturity 5 years
coupon 6 %
Time to maturity
5 years
Instrument-specific parameters:
Long/short position, etc.
Short-position FRA
Duration 1 month
instrument-specific parameters:
Long / short position, etc.
In this example, a fixed-rate-receiver swap is decomposed in a long
position, in which the bank receives from the swap counterparty a fixed
coupon of 5 percent and pays a variable 3-month London interbank offered rate (LIBOR) with monthly interest-rate resets.
2.7.2 Interest-Rate Risks
This subsection describes the standard framework for measuring the risk
of holding or taking positions in debt securities and other interest-raterelated instruments in the trading book. The trading book itself is not discussed in detail here.87
The instruments covered include all fixed-rate and floating-rate debt
securities and instruments that behave like them, including nonconvertible preference shares.88 Convertible bonds—i.e., debt issues or preference
shares that are convertible, at a stated price, into common shares—are
treated as debt securities if they trade like debt securities and as equities if
they trade like equities. The basis for dealing with derivative products is
considered later under Treatment of Options (Section 2.7.6). The minimum capital requirement is expressed in terms of two separately calculated charges, one applying to the specific risk of each security, whether it is
a short or a long position, and the other to the interest-rate risk in the portfolio (termed general market risk), where long and short positions in different securities or instruments can be offset. In computing the interest-rate
risk in the trading book, all fixed-rate and floating-rate debt securities and
instruments, including derivatives, are to be included, as well as all other
positions that present risks induced by interest rates.
The capital requirements for interest-rate risks are composed of two
elements, which are to be computed separately:
Requirements applying to specific risk. All risks that relate to
factors other than changes in the general interest-rate structure
are to be captured and subjected to a capital charge.
Requirements applying to market risk. All risks that relate to
changes in the general interest-rate structure are to be captured
and subjected to a capital charge.
The capital requirements applying to specific risks are to be computed separately for each issuer and those applying to general market
risk, per currency. An exception exists for general market risk in foreign
currencies with little business activity.
Should interest-rate instruments present other risks in addition to
the interest-rate risks dealt with here, such as foreign-exchange risks,
these other risks are to be captured in accordance with the related provisions as outlined in Part A.1-4 of the amendment. Mapping of Positions
The systems of measurement shall include all derivatives and off-balancesheet instruments in the trading book that are interest-rate sensitive. These
are to be presented as positions that correspond to the net present value of
the actual or notional underlying value (contract volume—i.e., market values of the underlying instruments) and subsequently are to be dealt with
for general market and specific risk in accordance with the rules presented.
Positions in identical instruments fulfilling the regulatory requirements and which fully or almost fully offset each other are excluded from
the computation of capital requirements for general market and specific
risks. In computing the requirements for specific risks, those derivatives
which are based on reference rates (e.g., interest-rate swaps, currency swaps,
forward rate agreements, forward foreign-exchange contracts, interest-rate
futures, and futures on an interest-rate index) are to be ignored.
Allowable Offsetting of Matching Positions
Offsetting is allowed for the following matching positions:
Positions that match each other in terms of amount in a futures or
forward contract and related underlying instrument (i.e., all
deliverable securities). Both positions, however, must be
denominated in the same currency. It should be kept in mind that
futures and forwards are to be treated as a combination of a long
and a short position (see Figure 2-7); therefore, one of the two
futures or forward positions remains when offsetting it against a
related spot position in the underlying instrument.
Opposite positions in derivatives that relate to the same
underlying instrument and are denominated in the same
currency. In addition, the following conditions must be met:
Market Risk
Futures. Offsetting positions in the notional or underlying
instruments to which the futures contract relates must be for
identical products and must mature within seven days of each
Swaps and forward rate agreements. The reference rate (for
floating-rate positions) must be identical, and the coupon must be
closely matched (i.e., within 15 basis points).
Swaps, forward rate agreements, and forwards. The next interestfixing date; or, for fixed coupon positions or forwards, the
residual maturity must correspond within the following limits:
• Less than one month from cutoff date—same day
• One month to one year from cutoff date—within seven days
• Over one year from cutoff date—within 30 days Futures, Forwards, and Forward
Rate Agreements
Futures, forwards and forward rate agreements (FRAs) are treated as a
combination of a long and a short position. The duration of a futures contract, a forward, or an FRA corresponds to the time until delivery or exercise of the contract plus (if applicable) the duration of the underlying value.
A long position in an interest-rate futures contract is, for example, to
be treated as follows:
A notional long position in the underlying interest-rate
instrument with an interest-rate maturity as of its maturity
A short position in a notional government security with the same
amount and maturity on the settlement date of the futures contract
If different instruments can be delivered to fulfill the contract, the institution can choose which deliverable financial instruments are to be fitted into the maturity ladder. In doing so, however, the conversion factors
set by the exchange are to be taken into consideration. In the case of a futures contract on an index of company debentures, the positions are to be
mapped at the market value of the notional underlying portfolio. Swaps
Swaps are treated as two notional positions in government securities
with respective maturities. For instance, when an institution receives a
floating interest rate and pays a fixed rate, the interest-rate swap is
treated as follows:
A long position in a floating-rate instrument with a duration that
corresponds to the period until the next interest-rate repricing date
A short position in a fixed-interest instrument with a duration
that corresponds to the remaining duration of the swap
Should one leg of a swap be linked to another reference value, such as
a stock index, the interest component is to be taken into consideration, with
a remaining duration (interest maturity) that corresponds to the duration of
the swap or the period until the next interest-rate repricing date, while the
equity component is to be handled according to the rules pertaining to equities. In the case of interest-rate and currency swaps, the long and short positions are to be considered in the computations for the applicable currencies.
Institutes with significant swap books, and which do not avail themselves of the offsetting possibilities dealt with previously under Mapping
of Positions (Section, may also compute the positions to be reported in the maturity or duration ladders with so-called sensitivity models or preprocessing models. The following possibilities exist:
Computation of the present value of the payment flows caused by each
swap by discounting each individual payment with a corresponding
zero-coupon equivalent. The net present values aggregated over
the individual swaps are slotted into the corresponding duration
band for low-interest-bearing bonds (i.e., coupon <3 percent) and
dealt with in accordance with the maturity method.
Computation of the sensitivity of net present values of the individual
payment flows on the basis of the changes in yield arrived at under the
duration method. The sensitivities are then slotted into the
corresponding time bands and dealt with in accordance with the
duration method. Specific Risk
The capital charge for specific risk is designed to protect against an adverse movement in the price of an individual security owing to factors related to the individual issuer. In measuring the risk, offsetting is restricted
to matched positions in the identical issue (including positions in derivatives). Even if the issuer is the same, no offsetting is permitted between
different issues, because differences in coupon rates, liquidity, call features, etc. mean that prices may diverge in the short run.
In computing the capital adequacy requirements for specific risk, the
net position per issuer is determined. Within a category—government,
qualified, other, or high-yield interest-rate instruments—all interest-rate instruments of the same issuer may be offset against each other, irrespective of
their duration. In addition, the individual institution is free to allocate all
interest-rate instruments of an issuer to that category corresponding to the
highest capital charge for an interest-rate instrument of the issuer in question contained in the relevant portfolio. The institution shall opt for one
method and apply this method consistently.
The capital requirements for specific risk are determined by multiplying the open position per issuer by the appropriate rate, as listed in Table 2-3.
Market Risk
T A B L E 2-3
Capital Requirements for Specific Risks of Interest-Rate Instruments
Interest-rate instruments
Capital Requirements
Qualified interest-rate instruments
Other interest-rate instruments
High-yield interest-rate instruments
The government category includes all forms of G-10 paper, including
bonds, Treasury bills, and other short-term instruments, but national authorities reserve the right to apply a specific risk weight to securities issued by certain foreign governments, especially securities denominated in
a currency other than that of the issuing government.
Qualified interest-rate instruments are those that meet one of the following criteria:
Investment-grade rating or higher from at least two credit-rating
agencies recognized by the local supervisory authority
Investment-grade rating or higher from one credit-rating agency
recognized by the local supervisory authority in the absence of a
lower rating from a rating agency recognized by the local
supervisory authority
Unrated, but with a yield to maturity and remaining duration
comparable with those of investment-grade-rated instruments of
the same issuer and trading on a recognized exchange or a
representative market
Rating agencies deemed to be recognized by the local regulator
would typically include those such as the following:
Dominion Bond Rating Service (DBRS), Ltd., Toronto
Fitch IBCA [International Bank Classification Agency], Duff &
Phelps, London
Mikuni & Company, Ltd., Tokyo
Moody’s Investors Service, Inc., New York
Standard & Poor’s (S&P) Ratings Services, New York
Thomson Bank Watch (TBW), Inc., New York
Accordingly, instruments with investment-grade ratings are longterm interest-rate instruments with a rating of BBB (DBRS, IBCA, Mikuni,
S&P, and TBW) or Baa (Moody’s) and higher, and short-term interest-rate
instruments with a rating such as Prime-3 (Moody’s), A-3 (S&P and
IBCA), M-4 (Mikuni), R-2 high (DBRS), or TBW-3 (TBW) and higher. Each
supervisory authority is responsible for monitoring the application of
these qualifying criteria, particularly in relation to the last criterion, where
the initial classification is essentially left to the reporting banks.
The other category receives the same specific risk charge as a privatesector borrower under the credit risk requirements (i.e., 8 percent). However, because this may in certain cases considerably underestimate the
specific risk for debt securities that have a high yield to redemption relative to government debt securities, each member country has the discretion to apply a specific risk charge higher than 8 percent to such securities
and to disallow offsetting for the purposes of defining the extent of general market risk between such securities and any other debt securities.
High-yield interest-rate instruments are those which meet one of the
following criteria:
Rating such as CCC, Caa, or lower for long-term or an equivalent
rating for short-term interest-rate instruments from a rating
agency recognized by the local supervisory authority
Unrated, but with a yield to maturity and remaining duration
comparable to those with a rating such as CCC, Caa, or lower for
long-term or an equivalent rating for short-term interest-rate
This means that long-term interest-rate instruments with a rating
such as CCC (DBRS, IBCA, Mikuni, S&P, and TBW), Caa (Moody’s), or
lower are deemed to be high-yield instruments. The high-yield rate is applicable to short-term interest-rate instruments if the rating is C (S&P), D
(IBCA), M-D (Mikuni), R-3 (DBRS), TBW-4 (TBW), or lower. General Market Risk
The capital requirements for general market risk are designed to capture
the risk of loss arising from changes in market interest rates. A choice between two principal methods of measuring the risk is permitted, a maturity method and a duration method. In each method, the capital charge is
the sum of four components:
The net short or long position in the whole trading book
A small proportion of the matched positions in each time band
(the vertical disallowance)
A larger proportion of the matched positions across different time
bands (the horizontal disallowance)
A net charge for positions in options, where appropriate
The capital requirements are computed for each currency separately
by means of a maturity ladder. Currencies in which the institution has a
Market Risk
small activity volume may be regrouped into one maturity ladder. In this
case, no net position value is determined, but an absolute position value
(i.e., all net long and short positions of all currencies in one time band) is determined by adding all the net positions together, irrespective of whether
they are long or short positions, and no further offsetting is permitted.
Maturity Method
When applying the maturity method, the equity requirements for general
market risk are computed as follows:
Slotting the positions valued at market into the maturity ladders. All
long and short positions are entered into the corresponding time
bands of the maturity ladder. Fixed-interest instruments are
classified according to their remaining duration until final
maturity, and floating-rate instruments according to the
remaining term until the next repricing date. The boundaries of
the maturity bands are defined differently for instruments whose
coupons are equal to or greater than 3 percent and those whose
coupons are less than 3 percent (see Table 2-4). The maturity
bands are allocated to three different zones.
T A B L E 2-4
Maturity Method: Time Bands and Risk-Weighting Factors
Coupon ≥ 3%
Up to
Coupon < 3%
1 month
Up to
Risk Weighting
1 month
1 month
3 months
1 month
3 months
3 months
6 months
3 months
6 months
6 months
12 months
6 months
12 months
1 year
2 years
1.0 year
1.9 years
2 years
3 years
1.9 years
2.8 years
3 years
4 years
3.6 years
3.6 years
4 years
5 years
3.6 years
4.3 years
5 years
7 years
4.3 years
5.7 years
7 years
10 years
5.7 years
7.3 years
10 years
15 years
7.3 years
9.3 years
15 years
20 years
9.3 years
10.6 years
10.6 years
12 years
12 years
20 years
20 years
20 years
Weighting by maturity band. In order to take account of the price
sensitivity in relation to interest-rate changes, the positions in the
individual maturity bands are multiplied by the risk-weighting
factors listed in Table 2-4.
Vertical offsetting. The net position is determined for each
maturity band from all weighted long and short positions. The
risk-weighted net position is subject to a capital charge of 10
percent for each maturity band. This serves to account for the
base and interest structure risk within each maturity band.
Horizontal offsetting. To determine the total net interest positions,
offsetting between opposed positions of differing maturities is
possible, whereby the resulting closed net positions in turn
receive a capital charge. This process is called horizontal offsetting.
Horizontal offsetting takes place at two levels: within each of the
three zones and between the zones.
Horizontal offsetting within the zones. The risk-weighted open net
positions of individual maturity bands are aggregated and offset
against each other within their respective zones to obtain a net
position for each zone. The closed positions arising from
offsetting are subject to a capital charge. This charge amounts to
40 percent for Zone 1 and 30 percent each for Zones 2 and 3.
Horizontal offsetting between various zones. Zone net positions of
adjacent zones may be offset against each other, provided they
bear opposing polarities (plus and minus signs). The resulting
closed net positions are subject to a capital charge of 40 percent.
An open position remaining after offsetting two adjacent zones
remains in its respective zone and forms the basis for further
offsetting, if applicable. Closed net positions arising from
offsetting between nonadjacent zones (Zones 1 and 3), if
applicable, are subject to a capital charge of 100 percent.
The result of the preceding calculations is to produce two sets of
weighted positions, the net long or short positions in each time band and
the vertical disallowances, which have no sign. In addition, however,
banks are allowed to conduct two rounds of horizontal offsetting, first between the net positions in each of three zones (0 to 1 year, 1 year to 4 years,
and 4 years and over), and subsequently between the net positions in the
three different zones. The offsetting is subject to a scale of disallowances
expressed as a fraction of the matched positions, as set out in Table 2-5.
The weighted long and short positions in each of the three zones may be
offset, subject to the matched portion, attracting a disallowance factor that
is part of the capital charge. The residual net position in each zone may be
carried over and offset against opposite positions in other zones, subject to
a second set of disallowance factors.
Market Risk
T A B L E 2-5
Components of Capital Requirements
1. Net long or net short positions, total
2. Vertical offsetting: weighted closed position in each
maturity band
Weighting Factor
3. Horizontal offsetting
Closed position in Zone 1
Closed position in Zone 2
Closed position in Zone 3
Closed position from offsetting between adjacent zones
Closed position from offsetting between nonadjacent zones
4. Add-on for option positions, if applicable (pursuant to
Sections 5.3.1, 5.3.2b, 5.3.2c, and 5.3.3 of the
Using the maturity method, the capital requirements for interest-rate
risk in a certain currency equal the sum of the components that require
weighting, as listed in Table 2-5.
Offsetting is to be applied only if positions with opposing polarities
(minus and plus signs) can be offset against each other within a maturity
band, within a zone, or between the zones.
Duration Method
Under the alternative duration method, banks with the necessary capability may, with the consent of their regulatory supervisors, use a more accurate method of measuring all of their general market risk by calculating
the price sensitivity of each position separately. Banks that elect to do so
must use the method on a continuous basis (unless a change in method is
approved by the national authority), and they are subject to supervisory
monitoring of the systems used.
Institutions that possess the necessary organizational, personnel,
and technical capacities may apply the duration method as an alternative
to the maturity method. If they opt for the duration method, they may
change back to the maturity method only in justified cases. The duration
method is to be used, in principle, by all branches and for all products.
As already mentioned, the price sensitivity of each financial instrument is computed separately under this method. It is also possible to split
the financial instrument into its payment flows and to take account of the
duration for each individual payment flow. The capital requirements for
general market risk are computed in the following manner:
Computation of price sensitivities. Price sensitivity is computed
separately for each instrument or its payment flows; the different
changes in yield dependent on duration, as listed in Table 2-6, are
subject to a capital charge. The price sensitivity is calculated by
multiplying the market value of the instrument or of its payment
flows by its modified duration and the assumed change in yield.
Entering price sensitivities into the time bands. The resulting
sensitivities are entered into one of the ladders. There are 15 time
bands, based on the duration of the instrument or its payment
flows, as shown in Table 2-6.
T A B L E 2-6
Duration Method: Maturity Bands and Assumed Changes in Yield
Up to
Change in Yield
1 month
1 month
3 months
3 months
6 months
6 months
12 months
1.0 years
1.9 months
1.9 years
2.8 years
2.9 years
3.6 years
3.6 years
4.3 years
4.3 years
5.7 years
5.7 years
7.3 years
7.3 years
9.3 years
9.3 years
10.6 years
10.6 years
12 years
12 years
20 years
20 years
Market Risk
Vertical offsetting. The vertical offsetting within the individual
time bands is to be effected in a manner analogous to that used
under the maturity method, whereby the risk-weighted closed
position for each maturity band is subject to a capital charge of 5
Horizontal offsetting. The horizontal offsetting between the time
bands is to be effected in a manner analogous to that used under
the maturity method.
Under the duration method, the required equity for general market
risk per currency is thus calculated from the sum of the net position, the
various offsets, and, where applicable, an add-on for option positions. Interest-Rate Derivatives
The measurement system should include all interest-rate derivatives and
off-balance-sheet instruments in the trading book that react to changes in
interest rates, (e.g., forward rate agreements, other forward contracts,
bond futures, interest-rate and cross-currency swaps, and forward foreign-exchange positions). Options can be treated in a variety of ways. A
summary of the rules for dealing with interest rate derivatives is set out
later under Treatment of Options (Section 2.7.6).
Calculation of Positions
Derivatives should be converted into positions in the relevant underlying
instruments (see Table 2-7) and become subject to specific and general
market risk charges as previously described. In order to calculate the standard formula as previously described, the amounts reported should be the
market value of the principal amount of the underlying instrument or of
the notional underlying instrument. When the apparent notional amount
of the instrument differs from the effective notional amount, banks must
use the effective notional amount.
Futures and forward contracts, including forward rate
agreements, are treated as a combination of a long and a short
position in a notional government security. The maturity of a
future or an FRA will be the period until delivery or exercise of
the contract, plus (where applicable) the life of the underlying
instrument. For example, a long position in a June three-month
interest-rate future (taken in April) is to be reported as a long
position in a government security with a maturity of five months
and a short position in a government security with a maturity of
two months. Where a range of deliverable instruments may be
delivered to fulfill the contract, the bank has flexibility to elect
which deliverable security goes into the maturity or duration
ladder but should take account of any conversion factor defined
T A B L E 2-7
Summary of Treatment of Interest-Rate Derivatives
Risk Charge*
General Market Risk Charge
Exchange-traded future
Government debt security
Yes, as two positions
Corporate debt security
Yes, as two positions
Index on interest rates
(e.g., LIBOR)
Yes, as two positions
Government debt security
Yes, as two positions
Corporate debt security
Yes, as two positions
Index on interest rates
(e.g., LIBOR)
Yes, as two positions
OTC forward
FRAs, swaps
Yes, as two positions
Forward foreign exchange
Yes, as one position in each currency
Either: Carve out together with the
associated hedging positions:
Government debt security
Simplified approach
Scenario analysis
Internal models
Corporate debt security
Index on interest rates
FRAs, swaps
General market risk change according
to the delta-plus method (gamma and
vega should receive separate capital
*This is the specific risk charge relating to the issuer of the instrument. Under the existing credit risk rules, there remains a
separate capital charge for the counterparty risk.
by the exchange. In the case of a future on a corporate bond
index, positions are included at the market value of the notional
underlying portfolio of securities.
Swaps are treated as two notional positions in government
securities with relevant maturities. For example, an interest-rate
swap under which a bank receives floating-rate interest and pays
fixed-rate interest is treated as a long position in a floating-rate
instrument of maturity equivalent to the period until the next
interest fixing and a short position in a fixed-rate instrument of
Market Risk
maturity equivalent to the residual life of the swap. For swaps
that pay or receive a fixed or floating interest rate against some
other reference price (e.g., a stock index), the interest-rate
component should be slotted into the appropriate repricing
maturity category, with the equity component being included in
the equity framework. The separate legs of cross-currency swaps
are to be reported in the relevant maturity ladders for the
currencies concerned.
Calculation of Capital Charges for Derivatives
Under the Standardized Methodology
Matched positions may be offset if certain conditions are fulfilled. Banks
may exclude from the interest-rate maturity framework altogether (for
both specific and general market risk) long and short positions (both actual and notional) in identical instruments with exactly the same issuer,
coupon, currency, and maturity. A matched position in a future or forward
and its corresponding underlying instrument may also be fully offset, and
thus excluded from the calculation; however, the leg representing the time
to expiry of the future should be reported. When the future or the forward
comprises a range of deliverable instruments, offsetting of positions in the
future or forward contract and its underlying instrument is permissible
only in cases in which there is a readily identifiable underlying security
that is the most profitable for the short-position trader to deliver. The price
of this security—sometimes called the cheapest to deliver—and the price of
the future or forward contract should, in such cases, move in close alignment. No offsetting is allowed between positions in different currencies;
the separate legs of cross-currency swaps or forward foreign-exchange
deals are to be treated as notional positions in the relevant instruments
and included in the appropriate calculation for each currency.
In addition, opposite positions in the same category of instruments
can, in certain circumstances, be regarded as matched and allowed to offset fully. To qualify for this treatment, the positions must relate to the same
underlying instruments,89 be of the same nominal value, and be denominated in the same currency.90
In addition, the following conditions have to be considered for the
calculation of the regulatory risk exposure:
Futures. Offsetting positions in the notional or underlying
instruments to which the futures contract relates must be for
identical products and must mature within seven days of each
Swaps and FRAs. The reference rate (for floating-rate positions)
must be identical, and the coupon must be closely matched (i.e.,
within 15 basis points).
Swaps, FRAs, and forwards. The next interest-fixing date or, for
fixed coupon positions or forwards, the residual maturity must
correspond within the following limits:
Less than one month hence—same day
One month to one year hence—within seven days
Over one year hence—within 30 days
Banks with large swap books may use alternative formulas for these
swaps to calculate the positions to be included in the maturity or duration
ladder. One method would be to first convert the payments required by the
swap into their present values. For this purpose, each payment should be
discounted using zero-coupon yields, and a single net figure for the
present value of the cash flows should be entered into the appropriate time
band, using procedures that apply to zero- (or low-) coupon bonds; these
figures should be slotted into the general market risk framework as set out
earlier. An alternative method would be to calculate the sensitivity of the
net present value implied by the change in yield used in the maturity or
duration method and allocate these sensitivities into the time bands.
Other methods that produce similar results could also be used. Such
alternative treatments will, however, be allowed only if:
The supervisory authority is fully satisfied with the accuracy of
the systems being used.
The positions calculated fully reflect the sensitivity of the cash
flows to interest-rate changes and are entered into the
appropriate time bands.
The positions are denominated in the same currency.
Interest-rate and currency swaps, FRAs, forward foreign-exchange
contracts, and interest-rate futures are not subject to a specific risk charge.
This exemption also applies to futures on an interest-rate index (e.g.,
LIBOR). However, in the case of futures contracts where the underlying
instrument is a debt security, or an index representing a basket of debt securities, a specific risk charge will apply according to the credit risk of the
issuer, as set out in the preceding paragraphs.
General market risk applies to positions in all derivative products in
the same manner as for cash positions, subject only to an exemption for
fully or very closely matched positions in identical instruments as defined. The various categories of instruments should be slotted into the maturity ladder and treated according to the rules identified earlier.
2.7.3 Equity Position Risk
To determine the capital requirements for equity price risks, all positions
in equities and derivatives, as well as positions whose behavior is similar
to equities (hereinafter these are referred to as equities) are to be included.
Market Risk
Shares in investment funds are also be dealt with like equities, unless they
are split into their component parts and the capital charges are determined in accordance with the provisions relating to each risk category.
Capital requirements for equity price risks comprise the following
two components, which are to be computed separately:
Specific risk requirements. Those risks which are related to the
issuer of the equities and cannot be explained by general market
fluctuations are to be captured and subjected to a capital charge.
General market risk requirements. Risks in the form of fluctuations
of the national equity market or the equity market of a single
monetary area are to be captured and subjected to a capital charge.
Should positions present risks other than the equity price risk dealt
with here, such as foreign-exchange risks or interest-rate risks, these are to be
captured in accordance with the corresponding sections of these guidelines. Mapping of Positions
Initially, all positions are to be marked to market. Foreign currencies must
be translated into the local currency at the current spot rate.
Index positions may be either treated as index instruments or split
into the individual equity positions and dealt with as normal equity positions. The institution shall decide on one approach and then apply it on a
consistent basis.
Derivatives based on equities and off-balance-sheet positions whose
value is influenced by changes in equity prices are to be recorded in the
measurement system at their market value of the actual or nominal underlying values (contract volume, such as market values of the underlying
Allowable Offsetting of Matched Positions
Opposite positions (differing positions in derivatives or in derivatives and
related underlying instruments) in each identical equity or each identical
stock index may be offset against each other. It is to be noted that futures
and forwards are to be treated as a combination of a long and a short position, and therefore the interest-rate position remains in the case of the
offsetting with a corresponding spot position in the underlying value.
Equity Derivatives
Except for options, which are dealt with under Futures and Forward Contracts, equity derivatives and off-balance-sheet positions that are affected
by changes in equity prices should be included in the measurement system.91 These include futures and swaps on both individual equities and
stock indexes. The derivatives are to be converted into positions in the relevant underlying instrument. The treatment of equity derivatives is summarized in Table 2-8.
T A B L E 2-8
Summary of Treatment of Equity Derivatives
Specific Risk*
General Market Risk
Exchange-traded or
OTC future
Individual equity
Yes, as underlying
Yes, as underlying
Either: Carve out together with the
associated hedging positions:
Individual equity
Simplified approach
Scenario approach
Internal models
General market risk charge according to
the delta-plus method (gamma and vega
should receive separate capital charges)
*This is the specific risk charge relating to the issuer of the instrument. Under the existing credit risk rules, there remains a
separate capital charge for the counterparty risk.
Futures and Forward Contracts
Futures and forward contracts are to be dealt with as a combination of a
long and a short position in an equity, a basket of equities, or a stock index,
on the one hand; and as a notional government bond, on the other. Equity
positions are thereby captured at their current market price. Equity-basket
or stock-index positions are captured at the current value of the notional
underlying equity portfolio, valued at market prices.
Equity swaps are also treated as a combination of a long and a short position. They may relate to a combination of two equity, equity-basket, or
stock-index positions or a combination of a equity, equity-basket, or stockindex position and an interest-rate position. Calculation of Positions
In order to calculate the standard formula for specific and general market risk, positions in derivatives should be converted into notional equity positions:
Market Risk
Futures and forward contracts relating to individual equities
should in principle be reported at current market prices.
Futures relating to stock indexes should be reported as the markedto-market value of the notional underlying equity portfolio.
Equity swaps are to be treated as two notional positions.92
Equity options and stock-index options should be either carved
out together with the associated underlying instruments or be
incorporated in the measure of general market risk described in
this section according to the delta-plus method. Calculation of Capital Charges
Several risk components have to be considered in the calculation of the
capital charges:
Measurement of specific and general market risk. Matched positions
in each identical equity or stock index in each market may be
fully offset, resulting in a single net short or long position to
which the specific and general market risk charges will apply. For
example, a future in a given equity may be offset against an
opposite cash position in the same equity. However, the interestrate risk arising from the future should be reported.
Risk in relation to an index. Besides general market risk, a further
capital charge of 2 percent is applied to the net long or short
position in an index contract comprising a diversified portfolio of
equities. This capital charge is intended to cover factors such as
execution risk. National supervisory authorities will take care to
ensure that this 2 percent risk weight applies only to welldiversified indexes and not, for example, to sectoral indexes.
Arbitrage. In the case of the futures-related arbitrage strategies
described later, the additional 2 percent capital charge previously
described may be applied to only one index with the opposite
position exempt from a capital charge. The strategies are:
When the bank takes an opposite position in exactly the same
index at different dates or in different market centers
When the bank has an opposite position in contracts at the same
date in different but similar indexes, subject to supervisory
oversight that the two indexes contain sufficient common
components to justify offsetting
When a bank engages in a deliberate arbitrage strategy, in which a
futures contract on a broadly based index matches a basket of stocks, it is
allowed to carve out both positions from the standardized methodology
on condition that:
The trade has been deliberately entered into and separately
The composition of the basket of stocks represents at least 90
percent of the index when broken down into its notional
In such a case the minimum capital requirement is 4 percent (i.e., 2
percent of the gross value of the positions on each side) to reflect divergence and execution risks. This applies even if all of the stocks comprising
the index are held in identical proportions. Any excess value of the stocks
comprising the basket over the value of the futures contract or excess
value of the futures contract over the value of the basket is to be treated as
an open long or short position.
If a bank takes a position in depository receipts against an opposite
position in the underlying equity or identical equities in different markets,
it may offset the position (i.e., bear no capital charge), but only on condition that any costs on conversion are fully taken into account. Any foreign
exchange risk arising out of these positions has to be reported. Specific Risk
To determine the capital requirements for specific risk, the net position by
issuer is determined; that is, positions with differing plus and minus signs
for the same issuer may be offset.
The capital charge corresponds to 8 percent of the net position per
For diversified and liquid equity portfolios, the requirements to support specific risks are reduced to 4 percent of the net position per issuer. A
diversified and liquid portfolio exists whenever the equities are quoted on
an exchange and no individual issuer position exceeds 5 percent of the
global equity portfolio or a subportfolio. The reference value to determine
the 5 percent limit in this context means the sum of the absolute values of
the net positions of all issuers. The global equity portfolio may be split into
two subportfolios so that one of the two subportfolios falls into the diversified and liquid category, and the specific risks within this portfolio need
only be subject to a 4 percent capital charge.
If stock-index contracts are not split into their components, a net long
or net short position in a stock-index contract representing a widely diversified equity portfolio is subject to a capital charge of 2 percent of equity. The
rate of 2 percent, however, shall not apply to sector indexes, for example. General Market Risk
The capital requirements for general market risk amount to 8 percent of
the net position per domestic equity market or per single currency zone. A
Market Risk
separate computation is to be made for each domestic equity market,
whereby long and short positions in instruments of differing issuers of the
same domestic market may be offset.
2.7.4 Foreign-Exchange Risk
All positions in foreign currency and gold are to be included in the computation of capital requirements for foreign-exchange risk. Determination of Net Position
The net position of an institution in a foreign currency is computed as the
sum of the following positions:
Net spot position. All assets less all liabilities and shareholders’
Net forward positions. All amounts outstanding less all amounts
to be paid within the framework of forward transactions
executed in this currency. The net present values are to be
included; that is, positions discounted with the current foreigncurrency interest rates. Because they relate to present values,
forward positions (including guarantees and similar instruments
that are certain to be called and are likely to be irrecoverable) are
also translated into the local currency at the spot rate and not the
forward rate.
Net amount of known, future income or expense that is fully hedged.
Future unhedged income and expense items can be taken into
consideration at the institution’s discretion, but thereafter on a
uniform and consistent basis.
Foreign-currency options.
In this manner, a net long or a net short position is arrived at. This is
translated at the respective spot rate into the local currency.
Basket currencies can be dealt with as a separate currency or broken
down into their currency components. The treatment, however, has to be
Positions in gold (cash and forward positions) are translated into a
common standard unit of measurement (in general, ounces or kilograms).
The net position is then valued at the respective spot price in the local currency. Any interest-rate or foreign-exchange risks arising from forward
gold transactions are to be recorded. Institutions may, in addition and at
their discretion, treat positions in gold as foreign-currency positions, but
then only in a uniform and consistent manner.
86 Exclusions
The following positions can be excluded from the computation:
Positions that were deducted from equity in the computation of
the equity base
Other participating interests that are disclosed at acquisition cost
Positions that demonstrably serve on an ongoing basis as a hedge
against foreign-currency fluctuations in order to secure the equity
ratio Determination of Capital Requirements
The capital requirements for foreign exchange and gold amount to 10 percent of the sum of net long or net short foreign-exchange positions,
whichever is greater, translated into the local currency, plus the net gold
position, ignoring plus or minus signs.
2.7.5 Commodities Risk
This section establishes a minimum capital standard to cover the risk of holding or taking positions in commodities, including precious metals, but excluding gold (which is treated as a foreign currency). A commodity is defined
as a physical product which is or can be traded on a secondary market—e.g.,
agricultural products, minerals (including oil), and precious metals.
The standard approach for commodities risk is suitable only for institutions with insignificant commodities positions. Institutions with significant
trading positions either in relative or absolute terms must apply the modelbased approach. In computing the capital charges for risks arising from raw
materials, in principle, the following risks must be taken account of.93
The price risk in commodities is often more complex and volatile
than that associated with currencies and interest rates. Commodity markets may also be less liquid than those for interest rates and currencies
and, as a result, changes in supply and demand can have a more dramatic
effect on price and volatility. Banks also need to guard against the risk that
arises when the short position falls due before the long position. Owing to
a shortage of liquidity in some markets, it might be difficult to close the
short position, and the bank might be squeezed by the market. These market characteristics can make price transparency and the effective hedging
of commodities risk more difficult.
For spot or physical trading, the directional risk arising from a
change in the spot price is the most important risk. However, banks using
portfolio strategies involving forward and derivative contracts are exposed to a variety of additional risks, which may well be larger than the
risk of a change in spot prices. These include:
Market Risk
The risk of changes in spot prices
The forward gap risk—that is, the risk of changes in the forward
price which cannot be explained by changes in interest rates
The base risk to capture the risk of changes in the price
correlation between two similar, but not identical, raw materials
In addition, banks may face credit counterparty risk on over-thecounter derivatives, but this is captured by the 1988 capital accord. The
funding of commodities positions may well open a bank to interest-rate or
foreign-exchange exposure; if so, the relevant positions should be included in the measures of interest-rate and foreign-exchange risk. When a
commodity is part of a forward contract (quantity of commodities to be received or delivered), any interest-rate or foreign-currency exposure from
the other leg of the contract should be reported. Positions which are
purely stock financing (i.e., a physical stock has been sold forward and the
cost of funding has been locked in until the date of the forward sale) may
be omitted from the commodities risk calculation, although they will be
subject to interest-rate and counterparty risk requirements.
The interest-rate and foreign-exchange risks arising in connection
with commodity transactions are to be dealt with in accordance with the
related sections of these guidelines. Determination of Net Positions
All commodity positions are to be allocated to a commodity group in accordance with Table 2-9. Within the group, the net position can be computed; that
is, long and short positions may be offset. For markets that have daily delivery dates, any contracts maturing within 10 days of one another may be offset.
Banks may choose to adopt the models approach. It is essential that
the methodology used encompasses the following risks:
Directional risk, to capture the exposure from changes in spot
prices arising from net open positions
Forward gap and interest rate risk, to capture the exposure to
changes in forward prices arising from maturity mismatches
Basis risk, to capture the exposure to changes in the price
relationship between two similar, but not identical, commodities
All commodity derivatives and off-balance-sheet positions that are
affected by changes in commodity prices should be included in this measurement framework. These include commodity futures, commodity
swaps, and options where the delta-plus method is used. (Banks using
other approaches to measure options risk should exclude all options and
the associated underlying instruments from both the maturity ladder approach and the simplified approach.) In order to calculate the risk, com-
T A B L E 2-9
Commodity Groups
Commodity Group
Crude oil
Allocation according to geographic criteria;
e.g., Dubai (Persian Gulf), Brent (Europe and
Africa), WTI (America), Tapis (Asia-Pacific), etc.
Refined products
Allocation according to quality; e.g., gasoline,
naphtha, aircraft fuel, light heating oil (incl.
diesel), heavy heating oil, etc.
Natural gas
Natural gas
Precious metals
Allocation according to chemical elements;
e.g., silver, platinum, etc.
Nonferrous metals
Allocation according to chemical elements;
e.g., aluminum, copper, zinc, etc.
Agricultural products
Allocation according to basic products, but
without differentiating between quality; e.g.,
soya (incl. soybeans, oil, and flour), maize,
sugar, coffee, cotton, etc.
modity derivatives should be converted into notional commodities positions and assigned to maturities as follows:
Futures and forward contracts relating to individual commodities
should be incorporated in the measurement system as notional
amounts of barrels, kilos, etc. and should be assigned a maturity
with reference to expiry date.
Commodity swaps in which one leg is a fixed price and the other
the current market price should be incorporated as a series of
positions equal to the notional amount of the contract, with one
position corresponding to each payment on the swap and slotted
into the maturity ladder accordingly. The positions would be long
positions if the bank is paying fixed and receiving floating, and
short positions if the bank is receiving fixed and paying floating.
Commodity swaps in which the legs are in different commodities
are to be incorporated in the relevant maturity ladder. No
offsetting is allowed in this regard except where the commodities
belong to the same subcategory. Commodity Derivatives
Futures and forward contracts are to be dealt with as a combination of a
long and a short position in a commodity on the one hand, and as a notional government bond on the other.
Market Risk
Commodity swaps with a fixed price on the one hand and with the
respective market price on the other are to be considered as a string of positions that correspond to the nominal value of the contract. In this context, each payment in the framework of the swap is to be regarded as a
position. A long position arises when the bank pays a fixed price and receives a variable price (short position: vice versa). Commodity swaps concerning different commodities are to be captured separately in the
corresponding groups.
Commodities futures and forwards are dealt with in a manner analogous to that of equity futures and forwards.
Banks may choose to adopt the models approach. It is essential that
the methodology used encompasses the following risks:
Directional risk, to capture the exposure from changes in spot
prices arising from net open positions
Forward gap and interest-rate risk, to capture the exposure to
changes in forward prices arising from maturity mismatches
Basis risk, to capture the exposure to changes in the price
relationship between two similar, but not identical, commodities
All commodity derivatives and off-balance-sheet positions that are
affected by changes in commodity prices should be included in this measurement framework. These include commodity futures, commodity
swaps, and options where the delta-plus method is used. (Banks using
other approaches to measure options risk should exclude all options and
the associated underlying instruments from both the maturity ladder approach and the simplified approach.) In order to calculate the risk, commodity derivatives should be converted into notional commodities
positions and assigned to maturities as follows:
Futures and forward contracts relating to individual commodities
should be incorporated in the measurement system as notional
amounts of barrels, kilos, etc. and should be assigned a maturity
with reference to expiry date.
Commodity swaps in which one leg is a fixed price and the other
the current market price should be incorporated as a series of
positions equal to the notional amount of the contract, with one
position corresponding to each payment on the swap and slotted
into the maturity ladder covering interest-rate-related
instruments accordingly. The positions would be long positions if
the bank is paying fixed and receiving floating, and short
positions if the bank is receiving fixed and paying floating.
Commodity swaps in which the legs are in different commodities
are to be incorporated in the relevant maturity ladder. No
offsetting is allowed in this regard except where the commodities
belong to the same subcategory, as previously defined.
90 Determination of Capital Requirements
The requirements to support commodities risk amount to 20 percent of the
net position per commodities group. In order to take account of the base
and time-structure risk, an additional capital charge of 3 percent of gross
positions (sum of the absolute values of long and short positions) of all
commodities groups is applied.
Treatment of Options Segregation
In the case of financial instruments containing an option component that
does not appear in a substantial and dominant manner, it is not compulsory
to deal with the option component thereof as an option. Convertible bonds
may be treated as bonds or as equities in accordance with the specific characteristics of each financial instrument. Bonds with a right of the issuer to
early redemption can be dealt with as pure bonds and entered into the corresponding time band based on the most probable date of repayment. Treatment of Financial Instruments with Option
If the option component appears in a substantial and dominant manner,
the financial instruments in question are to be dealt with by one of the following methods:
Analytical breakdown into option and underlying instrument
Approximation of the risk profiles by means of synthetic
portfolios of options and basis instruments Approach to Compute Capital Requirements
In recognition of the wide diversity of banks’ activities in options and
the difficulties of measuring price risk for options, several alternative
approaches are permissible at the discretion of the national supervisory
Those banks which solely use purchased options are free to use
the simplified approach, unless all their written option positions
are hedged by perfectly matched long positions in exactly the
same options, in which case no capital charge for market risk is
Those banks which also write options are expected to use one of
the intermediate approaches or a comprehensive risk
management model approach. The more significant its trading,
the more the bank will be expected to use a sophisticated
Market Risk
In the simplified approach, the positions for the options and the associated underlying instrument, cash, or forward are not subject to the
standardized methodology but rather are carved out and subject to separately calculated capital charges that incorporate both general market risk
and specific risk. The risk numbers thus generated are then added to the
capital charges for the relevant category—that is, interest-rate-related instruments, equities, foreign exchange, and commodities. The delta-plus
method uses the sensitivity parameters or “Greek letters” associated with
options to measure their market risk and capital requirements. Under this
method, the delta-equivalent position of each option becomes part of the
standardized methodology, with the delta-equivalent amount subject to
the applicable general market risk charges. Separate capital charges are
then applied to the gamma and vega risks of the option positions. The scenario approach uses simulation techniques to calculate changes in the
value of an options portfolio for changes in the level and volatility of its
associated underlying instruments. Under this approach, the general market risk charge is determined by the scenario grid (i.e., the specified combination of underlying and volatility changes) that produces the largest
loss. For the delta-plus method and the scenario approach, the specific risk
capital charges are determined separately by multiplying the delta equivalent of each option by the specific risk weights.
Three approaches are admissible for the computation of capital requirements on option positions: the simplified procedure for institutions
that use only purchased options, the delta-plus method, and scenario
analysis for all other institutions.
Simplified Approach
In the case of the simplified approach, options are not to be included
under the standard approach in regard to specific risk and general market
risk, but they are subject to capital requirements computed separately. The
risk values so computed are then added to the capital requirements for the
individual categories—that is, interest-rate instruments, equities, foreign
exchange, gold, and commodities.
Purchased call and put options. The capital requirements
correspond to the smaller of:
The market value of the option
The market value of the underlying instrument (contract volume,
i.e., market values of the underlying instruments) multiplied by
the sum of the rates for general market risk and (if applicable) for
specific market risk in relation to the underlying instrument.
Long cash position and purchased put option or short cash position and
purchased call option. The capital requirements correspond to the
market value of the underlying instrument (contract volume, i.e.,
market values of the underlying instruments) multiplied by the
sum of the rates for general market risk and (if applicable) for
specific risk in relation to the underlying instrument less the
intrinsic value of the option. The total requirement, however,
cannot be a negative value. The corresponding underlying
instruments are no longer to be included in the standard method.
(See Table 2-10.)
Intermediate Approach: Delta-Plus Method
Banks that write options are allowed to include delta-weighted options
positions within the standardized methodology. If options are dealt with
in accordance with the delta-plus method, they are to be mapped as positions that correspond to the market value of the underlying instrument
(contract volume, i.e., market values of the underlying instruments) multiplied by the delta (sensitivity of the option price in relation to changes in
the price of the underlying instrument). Depending on the underlying instrument, they are included in the computation of capital requirements for
specific and general market risk. As the risks of options are, however, inadequately captured by the delta, institutions must also measure the
T A B L E 2-10
Simplified Approach: Capital Charges
Long cash and long put
Short cash and long call
The capital charge is the market value of the
underlying security* multiplied by the sum of
specific and general market risk charges† for
the underlying security less the amount the
option is in the money (if any) bounded at zero.‡
Long call or long put
The capital charge is the lesser of:
The market value of the underlying security
multiplied by the sum of specific and general
market risk charges for the underlying security
The market value of the option
*In some cases, such as foreign exchange, it may be unclear which side is the underlying security; this should be taken to
be the asset that would be received if the option were exercised. In addition, the nominal value should be used for items
where the market value of the underlying instrument could be zero—caps and floors, swaptions, etc.
Some options (e.g., where the underlying security is an interest rate, a currency, or a commodity) bear no specific risk but
specific risk will be present in the case of options on certain interest-rate-related instruments (e.g., options on a corporate
debt security or corporate bond index) and for options on equities and stock indexes. The charge under this measure for
currency options will be 8 percent and for options on commodities 15 percent.
For options with a residual maturity of more than six months, the strike price should be compared with the forward, not
current, price. A bank unable to do this must take the in-the-money amount to be zero.
Where the position does not fall within the trading book (i.e., options on certain foreign-exchange or commodities
positions not belonging to the trading book), it may be acceptable to use the book value instead.
Market Risk
gamma risk (risk resulting from nonlinear relationships between option
price changes and changes in the underlying instrument) and vega risk
(risk resulting from the sensitivity of the option price to fluctuations of
volatility of the underlying instrument).
Delta risk. Capital requirements for delta risk on options with
interest-rate instruments, equities, foreign exchange, and
commodities are based on the delta-weighted positions.
In computing the general market risk, delta-weighted options on
debentures or interest rates are allocated to the time bands for interest-rate
instruments and (if applicable) also for computing specific risk. Options
on derivatives are to be mapped twice, like the corresponding derivatives
themselves. Thus, an April purchase of a June call option on a three-month
interest-rate future—on the basis of its delta equivalent—will be considered as a long position with a maturity of five months and as a short position with a maturity of two months. The written option will similarly be
entered as a long position with a maturity of two months and a short position with a maturity of five months.
Options on equities, foreign exchange, gold, and commodities will also
be incorporated into the measurement values as delta-weighted positions.
Gamma risk. For each individual option, a gamma effect, as
defined here, is to be computed:
Gamma effect = 0.5 ⋅ γ ⋅ δ2
where γ designates gamma and δ the change in the underlying
value of the option. δ is computed by multiplying the market
value of the (notional) underlying value (contract volume, i.e.,
amount receivable of the underlying value or nominal value) by
the following factors:
Interest-rate options: risk weight in accordance with Table 2-4
[dependent on the maturity of the (notional) underlying
Options on equities or stock indexes: 8 percent
Options on foreign exchange or gold: 10 percent
Options on commodities: 20 percent
A net gamma effect is to be computed from the gamma effects for the
same categories of underlying instruments. The individual categories are
defined as follows:
Interest-rate instruments of the same currency and the same time
Equities and stock indexes of the same national market or the
same currency zone
Foreign currencies of each identical currency pair
Only the negative net gamma effects are to be included in the computation of required equity and to be summed as absolute values to arrive
at the total capital requirement.
The method of computing the gamma capital requirements presented here takes into account only general market risk. Banks that possess significant positions in options on specific equities or debt
instruments must, however, take specific risks into consideration in computing gamma effects.
Vega risk. For each individual option, a vega effect, as defined
here, is to be computed:
Vega effect = 0.25 ⋅ ν ⋅ volatility
where ν designates the value of vega.
For each category of underlying instruments, a net vega effect is to
be computed by addition of all vega effects of long positions (purchased
options) and subtraction of all vega effects of short positions (sold options). The total capital requirements for the vega risk subject to a capital
charge result from the aggregation of the sum of absolute values of net
vega effects computed for each category.
The computation of vega effects is to be made based on implicit
volatilities. In the case of illiquid underlying instruments, other methods
may be used on an exception basis to determine the volatility structure.
Intermediate Approach: Scenario Method
More sophisticated banks also have the right to base the market risk capital charge for options portfolios and associated hedging positions on scenario matrix analysis. This is accomplished by specifying a fixed range of
changes in the option portfolio’s risk factors and calculating changes in
the value of the option portfolio at various points along this grid. For the
purpose of calculating the capital charge, the bank revalues the option
portfolio using matrices for simultaneous changes in the option’s underlying rate or price and in the volatility of that rate or price. A different matrix is set up for each individual underlying instrument, as previously
defined. As an alternative, at the discretion of each national authority,
banks that are significant traders in options are permitted to base the calculation for interest-rate options on a minimum of six sets of time bands.
Market Risk
When using this method, no more than three time bands should be combined into any one set.
In computing the capital requirements for options and related hedging
positions using scenario analysis, the potential change in value for all possible combinations of changes in the underlying instrument or rate (dimension
1) and volatility (dimension 2), within the framework of a separate standard
matrix, is to be computed for each category of underlying instruments or
rates.94 In the case of interest-rate instruments, it is possible to carry out a separate analysis not for the instruments of each time band but to summarize the
time bands into groups. However, a maximum of three time bands may
grouped together, and at least six different groups must be formed. For
foreign-exchange options in the scenario definition, the arbitrage relationship between the underlying instruments may be taken into consideration.
In such cases, the scenarios can be defined uniformly against the U.S. dollar.
The dimensions of the matrices to be used are defined as follows:
Change in value of underlying instrument or rate (dimension 1). The
computations are to be made within the range for at least seven
different changes in value (including a change of 0 percent),
where the assumed changes in value are at equally spaced
intervals. The ranges are to be defined as follows:
Interest-rate options: Plus or minus the change in yield, in
accordance with Table 2-6. Should several time bands be
regrouped, the highest of the rates of the regrouped time bands
shall apply for the group.
Options on equities and stock indexes: ⫾8 percent.
Options on foreign exchange and gold: ⫾10 percent.
Options on commodities: ⫾20 percent.
Computations on the basis of these value changes take into account
only general market risk, not specific risk. The requirement for
specific risk is thus to be computed separately, based on the deltaweighted positions (cf. secs. 1.2 and 1.3 of the 1996 amendment).
Change in volatility (dimension 2). In regard to the variation in
volatility, computations are to be conducted for at least three
points: an unchanged volatility as well as relative changes in
volatility of ⫾25 percent each.
After the computation of the matrix, each cell contains the net gain
or loss of options and related hedging positions. The capital requirement
computed for each category of underlying instrument corresponds in this
case to the greatest of the losses contained in the matrix.
The scenario analysis is to be made based upon implicit volatilities.
In the case of illiquid underlying instruments, other methods may be used
on an exception basis to determine the volatility structure.
2.7.7 Criticisms of the Standard Approach
Although the standard approach aims to identify banks with unusual exposure, it is still beset by problems, such as duration, diversification, interdependencies of market risk and credit risk, and qualitative requirements.
The duration of some instruments cannot be easily identified.
Mortgages, for instance, contain prepayment options that allow
the homeowner to refinance the loan if interest rates fall.
Conversely, homeowners will make payments over a longer
period if interest rates increase. The effective duration of
mortgages thus changes with the level of interest rates and the
history of prepayments for a mortgage pool. Assigning a duration
band to one of these instruments becomes highly questionable.
More generally, the risk classification is arbitrary. The capital
charges of 8 percent are applied uniformly to equities and
currencies (and gold) without regard for their actual return
The standard approach does not account for diversification across
risks. Low correlations imply that the risk of a portfolio can be
much less than the sum of individual component risks. This
diversification effect applies across market risks or across
different types of financial risks. Diversification across market
risks is the easiest to measure. Historical data are available; they
reveal that correlations across sources of risk generate
diversification and lower the total risk. These diversification
benefits are not recognized by simply aggregating across risk
factors. Similarly, exchange movements are not perfectly
correlated, nor are movements between interest rates and
exchange rates. Assuming perfect correlations across various
types of risks overestimates portfolio risk and leads to capital
adequacy requirements that are too high.
Correlations across different types of risks are more difficult to
deal with. Most notably, default risk may be related to interestrate risk. This is true for most floating-rate instruments (such as
adjustable-rate mortgages, where borrowers may default should
interest rates increase to insufferable amounts).
At times, even credit rating agencies have overlooked the effect
of market risk on the possibility of default. A prime example is
the Orange County bankruptcy in December 1994. At that
time, S&P’s and Moody’s long-term credit ratings for the
county were close to the highest possible—AA and Aa1,
respectively—in spite of more than $1 billion in unrealized
losses in the investment pool. The agencies claimed to have
Market Risk
conducted a thorough examination of the county’s finances,
yet they remained unaware of the impending cash crisis. This
occurred because the agencies focused only on credit risk—that
is, the possibility that a borrower could fail to repay. The
rating agencies failed to recognize that market risk can lead to
credit risk.
In April 1995, the Basel Committee presented a major extension of the
market risk models.95 For the first time, it gave banks the option of using
their own risk measurement models to determine their capital charge.
This decision stemmed from a recognition that many banks have developed sophisticated risk management systems, in many cases far more
complex than can be dictated by regulators. As for institutions lagging behind the times, this proposal provided a further impetus to create sound
risk management systems.
To use this approach, banks have to satisfy various qualitative requirements, including regular review by various management levels
within the bank and by regulators.
To summarize, the general market risk charge on any day t is:
1 60
MRCt = max k − ᎏ ⋅ 冱 VaR t − i , VaR t − 1
60 i = 1
where k is the multiplication factor determined by the supervisory authority, which can be set higher than its minimum of 3 if the supervisor is
not satisfied with the bank’s internal risk model.
To obtain total capital adequacy requirements, banks add their credit
risk charges to their market risk charges applied to trading operations.
Upon application, the local supervisory authority can authorize an institution to compute the capital requirements for market risks by means of
risk aggregation models specific to each institution.
Risk aggregation models are statistical processes used to determine
the potential changes in the value of portfolios on the basis of changes in
the factors that determine such risks. In this connection, value at risk (VaR)
is defined as that value which represents the maximum potential change
in value of the total position, given a certain confidence level during a predetermined period of time.
The equity requirements for interest-rate and equity price risks in the
trading book, and for foreign-exchange and commodity risks throughout
an institution, result from the aggregation of VaR-based capital charges
and any applicable additional requirements for specific risks on equity
and interest-rate instruments.
Conditions for and Process
of Granting Approval
Should an institution desire to apply the model-based approach, it should
make application to the local supervisory authority and submit documentation demanded by that authority.
The local supervisory authority shall base its decision concerning
its consent to use the model-based approach on the results of testing
conducted under its aegis together with the banking law auditors. Furthermore, the local supervisory authority can base its decision on the review results of foreign supervisory authorities, other banking law
auditors aside from those of the applicant, or other independent professional experts.
The approval to use the model-based approach is dependent on certain conditions.
The costs associated with testing the model during the preapproval
phase, as well as any subsequent necessary testing, are to be borne by the
The local supervisory authority shall grant approval for the use of
the model-based approach only if the following conditions have been met
on a continual basis:
The institution possesses a sufficient number of staff who are
familiar with complex models not only in the area of trading, but
also in risk control, internal auditing, and back-office functions.
The areas of trading, back office, and risk control possess an
adequate electronic data processing (EDP) infrastructure.
The risk aggregation model, in relation to the specific activities of
the institution (composition of its trading book and its role within
the individual markets—market maker, dealer, or end user), is
constructed on a sound concept and is correctly implemented.
The preciseness of measurement of the risk aggregation model is
The local supervisory authority can demand that the risk aggregation model first be monitored during a specific time frame and tested
under real-time conditions before it is implemented for the computation
of capital requirements for market risks to ensure that the following conditions are met:
The risk factors set as minimum requirements are taken account
of by the risk aggregation model.
The risk aggregation model corresponds to the set minimum
quantitative requirements.
The set minimum qualitative requirements are complied with.
Market Risk
After granting approval for the use of the model-based approach,
the local supervisory authority is to be notified whenever:
Significant modifications are made to the risk aggregation model.
The risk policy is changed.
The local supervisory authority shall decide whether and which further verification is necessary.
2.8.2 VaR-Based Components
and Multiplication Factor
The internal model proposal is based on the following approach:
The computation of VaR shall be based on a set of uniform
quantitative inputs.
A horizon of 10 trading days, or two calendar weeks, shall be
A 99 percent confidence interval is required.
An observation period based on at least a year of historical data
and updated at least once a quarter shall be used.
Correlations can be recognized in broad categories (such as fixed
income) as well as across categories (e.g., between fixed income
and currencies). As discussed before, this is an improvement over
previous proposals.
The capital charge shall be set as the higher of the previous day’s
VaR or the average VaR over the last 60 business days, times a multiplication factor. The exact value of this factor is to be determined by the local
regulators, subject to an absolute floor of 3. This factor is intended to provide additional protection against environments that are much less stable
than historical data would lead one to believe.
A penalty component shall be added to the multiplication factor if
backtesting reveals that the bank’s internal model incorrectly forecasts
risks. The purpose of this factor is to give incentives to banks to improve
the predictive accuracy of the models and to avoid overly optimistic projections of profits and losses due to model fitting. As the penalty factor
may depend on the quality of internal controls at the bank, this system is
designed to reward internal monitoring, as well as to develop sound risk
management systems.
The VaR-based equity requirement on a certain day corresponds to
the greater of the following two amounts:
The VaR computed within the framework of the model-based
approach for the portfolio held on the preceding day
The average of the daily VaR values computed using the modelbased approach for the preceding 60 trading days multiplied by
the multiplication factor for the specific institution as fixed by the
local supervisory authority.
The multiplication factor for each specific institution shall be at least
3. Its precise size will depend on the following:
The fulfillment of the qualitative minimum requirements
The preciseness of forecasting by the risk aggregation model,
which is to be tested using so-called backtesting
2.8.3 Requirement for Specific Risks
Institutions that model specific risks neither in the form of residual risks
nor in the form of event and default risks shall determine capital requirements for specific risks in accordance with the standard approach.
Institutions that model specific risks in accordance with the prerequisites, but which in doing so limit themselves to capturing residual risks,
and do not capture event and default risks at all or only partially, are subject to additional capital requirements for the specific risks of equity and
interest-rate instruments. At the discretion of the institution, these may be
determined using one of the following two approaches:
Amount of VaR for equity and interest-rate portfolios
Amount of VaR for the specific risks inherent in the equity and
interest-rate portfolio
To determine the additional requirements, the amount of specific
risk captured by the risk aggregation model for equity or interest-rate
portfolio shall, in this case, correspond to one of the following:
The increase in VaR for the related subportfolio caused by the
inclusion of specific risks
The difference between the VaR for the related portfolio and the
VaR, which ensues when all positions are substituted by positions
whose fluctuation in value is determined exclusively through
fluctuations of share market index or the reference interest-rate
The result of the analytical separation of general market risk from
specific risk within the framework of a certain model
For the purposes of determining these additional capital requirements, the general market risk for equities is to be defined by means of a
single risk factor: a representative market index or the first factor or a linear combination of factors for the purposes of an empirical factor model.
Market Risk
For interest-rate instruments, the general market risk shall correspond to
the fluctuation of the reference curve per currency based upon an established liquid market.
The institution must opt for a method for determining the additional
requirements for specific risks and apply this method on a continual basis.
Should an institution provide the local supervisory authority with
evidence that not only residual risks but also event and default risks are
fully modeled, it may be dispensed from additional capital requirements
for specific risks.
2.8.4 Combination of Model-Based
and Standard Approaches
Institutions wishing to use internal models must in principle possess a
risk aggregation model which, at minimum, covers all risk factor categories (foreign exchange, interest rates, equity prices, and commodity
prices) with respect to general market risks.
During the phase when an institution is migrating to the modelbased approach, the local regulator can allow it to combine the modelbased and standard approaches under the condition that the same
approach is applied within the same risk factor category, i.e., either the
model-based or standard approach.
If positions in a certain risk factor category (such as commodities
risk) are absolute and insignificant when considered relatively, the local
regulator may also allow an institution not to integrate these into the
model-based approach, but to deal with them separately in accordance
with the standard approach.
If the model-based and standard approaches are combined, the total
capital requirement for market risks is arrived at through a simple addition of the capital requirements for each component.
2.8.5 Specification of Market Risk Factors
to Be Captured
An important part of a bank’s internal market risk measurement system is
the specification of an appropriate set of market risk factors, i.e., the market rates and prices that affect the value of the bank’s trading positions.
The risk factors contained in a market risk measurement system should be
sufficient to capture the risks inherent in the bank’s portfolio of on- and
off-balance-sheet trading positions. Although banks will have some discretion in specifying the risk factors for their internal models, the following guidelines should be fulfilled.
In principle, the risk aggregation model must take into consideration
all risk factors that impact the relevant positions of the institution. An ex-
ception exists for the specific risks of equity and interest-rate instruments
whose capital requirements may also be computed in accordance with the
standard approach.
The following minimum requirements apply for the individual risk
factor categories:
Interest-rate risks. The interest-structure risks in each currency in
which notable interest-rate-sensitive positions are held are to be
captured. In this respect, the following shall apply:
The modeling of the interest maturity structure is to be made in
accordance with a recognized method.
The number and distribution of the time bands must be appropriate
to the size and structure of operations; there must be six at a
The risk aggregation model must capture spread risks. These
exist in that changes in value of cash flows with similar maturity
and currency but issuers of different rating categories are not
fully correlated.
Foreign-exchange risks. Risk factors for the exchange rates
between the domestic currency and each foreign currency in
which the institution holds a significant exposure are to be taken
into consideration.
Equity price risks. The risk aggregation model must take into
consideration a risk factor (e.g., a stock market index) at least for
each national market or single currency zone in which significant
positions are held. Risk factor definitions based on sector or
branch indexes are also possible.
Commodities risks. Risk factors are to be modeled for each group
of commodities. In addition, the risk aggregation model must
take into consideration risks in the form of so-called convenience
yields—i.e., different developments in spot and forward prices
not induced by interest rates.
Risks of option positions. For options, the VaR measure, in
addition to delta risks, must capture at least the following risks:
Gamma risks. Risks arising from nonlinear relationships between
option price changes and changes in the price of the underlying
Vega risks. Risks arising from the sensitivity of option prices
against changes in volatility of the underlying instrument.
Institutions with large and complex option portfolios must take
appropriate account of volatility risks of option positions
according to different maturities.
Market Risk
Specific risks of equity and interest-rate instruments. Specific risks
equate those parts of aggregate volatility which relate to
occurrences in connection with the issuer of the individual
instruments and which cannot be explained by general market
risks. To determine the capital requirements, the following
further differentiation is to be made:
Specific risks in the form of residual risks. A residual risk represents
that part of the volatility of price fluctuations of equity and
interest-rate instruments which cannot be explained empirically
by general market factors within the context of a single- or
multiple-factor model.
Specific risks in the form of event and default risks. Specific event
risks correspond to the risk that the price of a certain equity or
interest-rate instrument changes abruptly as a result of
occurrences in connection with the issuer and to an extent which
cannot be explained as a general rule by the analysis of historic
price fluctuations. In addition to default risk, any abrupt price
fluctuations in connection with shocklike occurrences—such as,
for instance, a takeover bid—constitute event risks.
An appropriate modeling of specific risks in the form of residual
risks presupposes that the model satisfies all quantitative and qualitative
minimum requirements, as well as that the following conditions are met:
The historic change in the portfolio value is explained to a large
The model demonstrably captures concentrations; i.e., it is
sensitive to fluctuations in the composition of the portfolio.
The model has proven itself to be robust even in periods of
strained market situations.
A complete capture of specific risks presupposes that residual risks as
well as event and default risks are captured by the risk aggregation model.
Minimum Quantitative Requirements
No specific type of risk aggregation model is prescribed for the determination of capital requirements for market risks. Institutions may determine
the VaR on the basis of variance-covariance models, historical simulations,
Monte Carlo simulations, and the like. The risk aggregation model, however, must fulfill the following quantitative minimum requirements:
Periodicity of computation. The VaR is to be computed daily on
the basis of the prior day’s positions.
Confidence level. The computation of VaR should be effected
using a one-tailed forecasting interval with a confidence level of
99 percent.
Holding period. In computing VaR, a change in the risk factors
corresponding to a change over a 10-day period is to be used.
Also allowed are VaR numbers which are, for instance,
determined on the basis of a holding period of 1 day and
converted to a value corresponding to a holding period of 10
days by multiplication by 10. Institutions with significant option
positions must, however, convert in due course to capturing in
the risk aggregation model the nonlinear relationship between
option price changes and changes in the price of the
corresponding underlying instrument by means of 10-day
changes in risk factors.
Historical observation period and updating of data sets. The
observation period for the forecasting of future changes and
volatilities in risk factors, including the correlation between
them which is at the basis of the VaR computation, must amount
to one year at least. Should the individual daily observations be
taken into consideration with individual weights in the
computation of volatility and correlations (weighting), the
weighted average observation period (weighted lag) must be at
least six months (i.e., the individual values in the weighted
average must be at least six months old). The data sets must be
updated at least each quarter unless market conditions require
immediate updating.
Correlations. The VaR computation may be effected by
recognizing empirical correlations both within the general risk
factor categories (i.e., interest rates, exchange rates, equity prices,
and commodity prices, including related volatilities) and between
the risk factor categories in case the correlation system of the
institution is based on sound concepts and correctly
implemented. The correlations are to be continuously monitored
with particular care. Above all, the impact on the VaR of abrupt
changes in correlations between the risk factor categories are to
be computed and evaluated regularly during stress testing.
Should the computation of VaR be effected without considering
empirical correlations between the general risk factor categories,
the VaR for the individual risk factor categories is to be
aggregated through addition.
Alan Greenspan was very explicit about stress testing, highlighting
its importance in the context of liquidity and systemic risk:
Market Risk
The use of internal models for risk analysis, and as the basis for regulatory
capital charges has become common so far as market risk is concerned.
While the limits of models, and the importance of the assumptions that must
be made to put them to use, have been reasonably well understood, those issues have been brought into sharp focus by the Asian crisis. For example,
firms now appreciate more fully the importance of the tails of the probability distribution of the shocks and of the assumptions about the covariance of
prices charges. The use of stress tests, which address the implications of extreme scenarios, has properly increased.96
Minimum Qualitative Requirements
The supervisory authorities are able to assure themselves that banks using
models have market risk management systems that are conceptually
sound and that are implemented with integrity. Accordingly, the supervisory authorities have specified a number of qualitative criteria that banks
have to meet before they are permitted to use a models-based approach.
The extent to which banks meet the qualitative criteria may influence the
level at which supervisory authorities set the multiplication factor. Only
those banks whose models are in full compliance with the qualitative criteria are eligible for application of the minimum multiplication factor. Integrity of Data
The institution shall demonstrate that it possesses sound, documented, internally tested, and approved procedures which ensure that all transactions are captured, valued, and prepared for risk measurement in a
complete, accurate, and timely manner. Manual corrections to data are to
be documented so that the reason and exact content of the correction may
be reconstructed. In particular, the following principles shall apply:
All transactions are to be confirmed daily with the counterparty.
The confirmation of transactions as well as their reconciliation is
to be effected by a unit independent of the trading department.
Differences are to be investigated at once.
A procedure must be in force which will ensure the
appropriateness, uniformity, consistency, timeliness, and
independence of the data used in the valuation models.
All positions are to be processed in a manner which ensures
complete recording in terms of risk. Independent Risk Control Department
The institution must possess a risk control department which has qualified employees in sufficient number, is independent of the trading activi-
ties, and reports directly to a member of the management team responsible for risk control.
Risk control shall support the following functions in particular:
Organization and implementation of risk monitoring systems
(trading and control systems).
Close control over daily operations (limits, profit and loss
statement, etc.) including measurement criteria for market risk.
Daily VaR computations, analyses, controls, and reporting:
Preparation of daily reports on the results of the risk aggregation
model, as well as analyses of the results, including the
relationship between VaR and trading limits.
Daily reporting to the responsible member of management.
Completion of regular backtesting.97
Completion of regular stress testing.
Testing and authorization of risk aggregation models, valuation
models for computing the daily profit and loss statement, and
models to generate input factors (e.g., yield-curve models).
Ongoing review and updating of the documentation for the risk
monitoring system (trading and control systems). Management
The following provisions shall apply to management for the purposes of
using the model-based approach:
The responsible member of management must be informed
directly on a daily basis, and in an appropriate manner, of the
results of the risk aggregation model, and he or she shall subject
these to a critical review.
The responsible member of management who evaluates the daily
reports of the independent risk-monitoring department must
possess the authority to reduce the positions of individual traders
as well as to reduce the overall risk exposure of the bank.
The responsible member of management must be informed
periodically of the results of backtesting and stress testing by the
risk control department, and he or she must subject these results
to critical review. Risk Aggregation Model, Daily Risk Management,
and System of Limits
The following principles shall apply for the relationship between the risk
aggregation model, daily risk control, and limits:
Market Risk
The risk aggregation model must be closely integrated into daily
risk control. In particular, its results must be an integral part of
the planning, monitoring, and management of the market risk
profile of the institution.
There must exist a clear and permanent relationship between the
internal trading limits and the VaR (as it is used to determine
capital requirements for market risks). The relationship must be
known by both dealers and management.
The limits are to be reviewed regularly.
The procedures to be followed in case the limits are exceeded,
and any applicable sanctions, must be clearly defined and
documented. Backtesting
An institution using the model-based approach must possess regular,
sound, documented, and internally tested procedures for backtesting. In
principle, backtesting serves the purpose of obtaining feedback on the
quality and precision of the risk measurement system.
The process of backtesting retrospectively compares the trading income during a defined period of time with the dispersion area of trading
income predicted by the risk aggregation model for that period. The goal
of the process is to be able to state, within certain probabilities of error,
whether the VaR determined by the risk aggregation model actually covers 99 percent of the trading outcome. For reasons of statistical reliability
of the assertions, the daily trading profits and the daily VaR are compared
over a longer observation period.
For the purposes of the model-based approach, a standardized backtesting process is required to determine the multiplier specific to the institution. Regardless, institutions should also use backtesting on a lower
level than that of the global risk aggregation model—for example, for individual risk factors or product categories—in order to investigate questions regarding risk measurement. In this manner, parameters other than
those of the standardized backtesting process can be used in backtesting.
Institutions which determine not only requirements for general market
risks but also those for specific risks by means of a risk aggregation model
must also possess procedures for backtesting which indicate the adequacy of
modeling specific risks. In particular, separate backtesting is to be conducted
for subportfolios (equity and interest-bearing portfolios) containing specific
risks, and the results are to be analyzed and reported upon demand to the
local supervisory authority as well as to the banking law auditors.
Backtesting is to be conducted with consideration given to the following standards in order to determine the multiplication factor specific
to the institution:
The test must be based on the VaR computed for the daily market
risk report. The only difference relates to the fact that a holding
period of 1 day, not 10 days, is subject to a capital charge.
The decision whether backtesting should be carried out on the
basis of actual trading results (i.e., inclusive of results of intraday
trading and inclusive of commissions), trading results from
which these items have been eliminated, or hypothetical trading
results determined by revaluation to market of the financial
instruments in the institution’s portfolio on the preceding day is
left, in principle, to each individual institution. The condition is
that the process may be declared to be sound, and the income
figures used must not systemically distort the test outcome. In
addition, a uniform process over the time period is to be applied;
i.e., the institution is not free to change the backtesting
methodology without consulting the local supervisory authority.
The sampling method applied is to be based on 250 prior
The daily VaR reported internally, as well as the trading result on the
day of computation, are to be documented in a manner that is irreversible
and that may be inspected at any time by the local supervisory authority
and the banking law auditors.
The institution shall daily compare the trading result with the VaR computed for the day before. Cases in which a trading loss exceeds that of the corresponding VaR are designated as exceptions. The review and documentation
of these exceptions (for observations for the 250 preceding trading days) is to
be undertaken at least each quarter. The result of this quarterly review is to be
reported to the local supervisory authority and the banking law auditors.
The increase in the multiplication factor specific to the institution
corresponds to the number of exceptions noted during the observation period of the preceding 250 trading days (Table 2-11). In the case of the increase of the multiplication factor dependent on backtesting, the local
supervisory authority can ignore individual exceptions if the institution
demonstrates that the exception does not relate to an imprecise (forecasting quality) risk aggregation model.
If there are more than four exceptions for the relevant observation
period before 250 observations are available, the local supervisory authority is to be notified immediately. From that day forward, the institution
must compute VaR with an increased multiplier until the local supervisory authority has made a final decision.
If an institution-specific multiplication factor greater than 3 should
be set as a result of backtesting, it is expected that the origin of the imprecise estimates of the risk aggregation model will be investigated and, if
possible, eliminated. The setting of the multiplier to 4 requires a compul-
Market Risk
T A B L E 2-11
Multiplication Factor Specific to the Institution
Number of Exceptions
Increase in Multiplication Factor
4 or fewer
10 or more
sory rapid and careful review of the model. The shortcomings are to be
eliminated swiftly. Otherwise, the conditions for using the model-based
approach will be deemed violated.
A reduction of the multiplication factor by the local supervisory authority will ensue only if the institution can demonstrate that the error has
been remedied and that the revised model presents an appropriate forecasting quality. Stress Testing
An institution using the model-based approach must apply regular,
sound, consistent, documented, and internally tested stress-testing procedures. Important goals of stress testing are to ascertain whether the equity
can absorb large potential losses and to derive possible corrective action.
The definition of meaningful stress scenarios is left, in principle, to
the individual institution. The following guidelines, however, shall apply:
Scenarios which lead to extraordinary losses or which render the
control of risks difficult or impossible are to be considered.
Scenarios with extreme changes in market risk factors and the
correlation between these (arbitrarily set scenarios or historic
scenarios corresponding to periods of significant market
turbulence) are to be applied.
Scenarios specific to the institution which must be considered
particularly grave in regard to the specific risk positions are to be
The analyses must capture liquidity aspects of market
disturbances in addition to extreme changes in market risk
factors and their intercorrelation.
The risks of all positions are to be included in stress testing,
especially option positions.
In addition to actual quantitative stress tests and analyses thereof,
lines of responsibility must exist to ensure that the outcome of stress testing
will trigger the necessary measures:
The results of stress testing must be periodically reviewed by the
responsible member of management and be reflected in the
policy and limits that are set by management and the internal
authority for direction, supervision, and control.
If certain weaknesses are uncovered through stress testing, steps
must be taken immediately to deal with these risks appropriately
(e.g., by hedging or by reduction of the risk exposure). Criticisms of the Internal Model Approach
The internal model approach has been highly welcomed and criticized at
the same time. This part of the accord has been severely criticized by the
International Swaps and Derivatives Association (ISDA). In particular, the
multiplication factor of 3 is viewed as too large. The ISDA showed that a
factor of 1 would have provided enough capital to cover periods of global
turmoil, such as the 1987 stock market crash, the 1990 Gulf War, and the
1992 European Monetary System (EMS) crisis. An even more serious criticism is that the method based on an internal VaR creates a capital requirement that is generally higher than the standard model prescribed by the
Basel Committee. Hence, the current approach provides a negative incentive to the development of internal risk models.
The debate on the appropriate risk measurement system took another
turn when the U.S. Federal Reserve Board proposed a precommitment approach to bank regulation in 1995. Under this third alternative, the bank
would precommit to a maximum trading loss over a designated horizon. This loss would become the capital charge for market risk. The supervisor would then observe, after, say, a quarterly reporting period,
whether trading losses exceeded the limit. If so, the bank would be penalized, which might include a fine, regulatory discipline, or higher future capital charges. Violations of the limits would also bring public
scrutiny to the bank, which provides a further feedback mechanism for
good management.
The main advantage of this “incentive-compatible” approach is that
the bank itself chooses its capital requirement. As Kupiec and O’Brien
have shown, this choice is made optimally in response to regulatory
penalties for violations.98 Regulators can then choose the penalty that will
induce appropriate behavior.
Market Risk
This proposal was welcomed by the ISDA, which argued that this
approach explicitly recognizes the links between risk management practices and firm-selected deployment of capital. Critics, in contrast, pointed
out that quarterly verification is very slow in comparison to the real-time
daily capital requirements of the Basel proposals. Others worried that dynamic portfolio adjustments to avoid exceeding the maximum loss could
exacerbate market movements, in the same way that portfolio insurance
supposedly caused the crash of 1987.
At this point, it is useful to compare the pros and cons of each method. The
first, the standard model method, is generally viewed as least adequate
because of the following factors:
Portfolio considerations. The model ignores diversification effects
across sources of risk.
Arbitrary capital charges. The capital charges are only loosely
related to the actual volatility of each asset category. This can
distort portfolio choices, as banks move away from assets for
which the capital charge is abnormally high.
Compliance costs. Given that many banks already run
sophisticated risk measurement systems, the standard model
imposes a significant additional reporting burden.
The second method, the internal model, addresses all of these issues.
It relies on the self-interest of banks to develop accurate risk management
systems. Internal VaR systems measure the total portfolio risk of the bank,
account for differences in asset volatilities, and impose only small additional costs. In addition, regulatory requirements will automatically
evolve at the same speed as risk measurement techniques, as new developments will be automatically incorporated into internal VaRs.
Unfortunately, from the viewpoint of regulators, the internal model
still has some drawbacks:
Performance verification. Supervisors are supposed to monitor
whether internal VaRs indeed provide good estimates of future
profits and losses in trading portfolios. As capital charges are
based on VaRs, there may be an incentive to artificially lower the
VaR figure to lower capital requirements; thus, verification by
regulators is important. The problem is that, even with a wellcalibrated model, there will be instances when losses will exceed
the VaR by chance (e.g., 5 percent of the time using a 95 percent
confidence level). Unfortunately, long periods may be needed to
distinguish between chance losses and model inaccuracies. This
issue makes verification difficult.
Endogenity of positions. The banks’ internal VaRs typically
measure risk over a short interval, such as a day. Extending these
numbers to a 10-day trading period ignores the fact that positions
will change, especially in response to losses or unexpectedly high
volatility. Therefore, measures of long-horizon exposure ignore
efficient risk management procedures and controls. Perhaps this
is why the ISDA found that the current approach appeared too
Note that these problems do not detract from the usefulness of VaR
models for corporate risk management. From the viewpoint of regulators,
however, the precommitment approach has much to recommend, because
it automatically accounts for changing positions. In addition, the risk coverage level is endogenously chosen by the bank, in response to the penalty
for failure, which creates fewer distortions in capital markets.
Unfortunately, all models suffer from a performance verification
problem. The regulator can compare only ex post, or realized, performance
to ex ante estimates of risk or maximum loss. Unless the maximum loss is
set extremely high, there always will be instances in which a loss will exceed the limit even with the correct model. The key then for regulators is
to separate good intentions and bad luck from reckless behavior.
2.11.1 The E.U. Capital Adequacy Directive
The history of capital adequacy requirements in Europe must be put in the
perspective of plodding movements toward European economic and political integration. The Single European Act of 1985 committed member
countries to achieving a free market in goods, services, capital, and labor.
To this end, the European Union’s Investment Services Directive (ISD),
which came into effect on January 1, 1996, swept away restrictions against
nonlocal financial services. Up until then, a securities firm that wanted to
do business in another European Union country had to abide by local
rules—for instance, having to establish separately capitalized subsidiaries
(and expensive offices) in foreign countries. In effect, this raised the cost of
doing business abroad and made Europe’s internal market less efficient
than it might otherwise have been.99
Under the new regulations, firms based in one E.U. country were authorized to carry out business in any other E.U. country. This was expected to lead to the general consolidation of office networks. For
instance, Deutsche Bank announced that its global investment banking activities would be centralized in London. Also, the centralization of risk
management would provide for better control of financial risks. In addi-
Market Risk
tion to efficiency gains, more competition was expected to drive down
transaction costs and increase the liquidity of European financial markets.
To discourage firms from rushing to set up shop in the country with the
lowest level of regulations, however, the European Union adopted Europewide capital requirements known as the Capital Adequacy Directive
(CAD I). The CAD, published in March 1993, laid down minimum levels of
capital to be adopted for E.U. banks and securities houses by January 1996.
In many ways, the CAD paralleled the Basel guidelines. It extended
the 1989 Solvency Ratio and Own Funds Directives, which were similar to
the 1988 Basel accord. The 1993 requirements were very similar and in
some cases identical to those laid out in the 1993 Basel proposal. The
amendment to incorporate market risks led to the updated version, CAD
II (April 1997), which allowed all E.U. institutions to run their own VaR
models for daily calculation.
There were some differences, however. First, the Basel guidelines
were aimed only at banks, not securities houses. Regulation of securities
houses is concerned mainly with orderly liquidation, while bank regulators aim to prevent outright failure. Second, the CAD II guidelines were
put into effect in 1996, whereas the Basel rules became effective in 1998,
which left a period during which European firms had to comply with a
separate set of guidelines.
New Capital Adequacy Framework
to Replace the 1988 Accord
The market risk approaches remained unchanged.100 Refer back to the discussion earlier in this chapter of the 1996 Amendment to the Capital Accord to Incorporate Market Risks (Section 2.6), which outlines the
quantitative approaches in detail.
In many ways, the regulation of nonbank financial intermediaries parallels that of banks. Each of these institutions must learn to deal effectively
with similar sources of financial risk.
Also, there is a tendency for lines of business to become increasingly
blurred. Commercial banks have moved into trading securities and provide some underwriting and insurance functions. The trading portfolios
of banks contain assets, liabilities, and derivatives that are no different
from those of securities houses. Therefore, trading portfolios are measured at market values, while traditional banking items are still reported at
book value. With the trend toward securitization, however, more and
more assets (such as bank loans) have become liquid and tradable.
2.12.1 Pension Funds
Although pension funds are not subject to capital adequacy requirements,
a number of similar restrictions govern defined-benefit plans. The current
U.S. regulatory framework was defined by the Employee Retirement Income Security Act (ERISA) promulgated in 1974. Under ERISA, companies
are required to make contributions that are sufficient to provide coverage
for pension payments. In effect, the minimum capital is the present value
of future pension liabilities. The obligation to make up for unfunded liabilities parallels the obligation to maintain some minimal capital ratio. Also,
asterisk weights are replaced by a looser provision of diversification and of
not taking excessive risks, as defined under the “prudent man” rule.
As in the case of banking regulation, federal guarantees are provided
to pensioners. In the United States, the Pension Benefit Guarantee Corporation (PBGC), like the Federal Deposit Insurance Corporation (FDIC),
charges an insurance premium and promises to cover defaults by corporations. Other countries have similar systems, although most other countries rely much more heavily on public pay-as-you-go schemes, in which
contributions from current employees directly fund current retirees. The
United States, Britain, and the Netherlands are far more advanced in their
reliance on private pension funds. Public systems in countries afflicted by
large government deficits can ill afford generous benefits to an increasingly aging population. As a result, private pension funds are likely to
take on increasing importance all over the world. With those will come the
need for prudential regulation.
2.12.2 Insurance Companies
Regulation of insurance companies is globally less centralized than that of
other financial institutions, whose insurance is regulated at the national
level. In the United States, the insurance industry is regulated at the state
level. As in the case of FDIC protection, insurance contracts are ultimately
covered by a state guaranty association. State insurance regulators set nationwide standards through the National Association of Insurance Commissioners (NAIC).
In December 1992, the NAIC announced new capital adequacy requirements for insurers. As in the case of the early 1988 Basel accord, the
new rules emphasized credit risk. For instance, no capital would be
needed to cover holdings of government bonds and just 0.5 percent for
mortgages, but 30 percent of the value of equities would have to be covered. This ratio was much higher than the 8 percent ratio required for
banks, which some insurers claimed put them at a competitive disadvantage vis-à-vis other financial institutions that were increasingly branching
out into insurance products.
Market Risk
In the European Union, insurance regulation parallels that of banks,
with capital requirements, portfolio restrictions, and regulatory intervention in cases of violation. For life insurance companies, capital must exceed 4 percent of mathematical reserves, computed as the present values
of future premiums minus future death liabilities. For non-life insurance
companies, capital must exceed the highest of about 17 percent of premiums charged for the current year and about 24 percent of annual settlements over the past three years.
2.12.3 Securities Firms
The regulation of securities firms is still evolving. Securities firms hold securities on the asset and liability sides (usually called long and short positions) of their balance sheets. Regulators generally agree that some
prudent reserve should be available to cover financial risks. There is no
agreement, however, as to whether securities firms should hold capital to
cover their net positions, consisting of assets minus liabilities, or their
gross positions, consisting of the sum of all long plus short positions.
The United States and Japan use the gross position approach, the
United Kingdom uses the net position, and the Basel Committee and the
European Union consider a variant of both approaches. The European
Union, for instance, required firms to have equity equal to 2 percent of
their gross positions plus 8 percent of their net positions as of 1996.
Dimson and Marsh compare the effectiveness of these approaches
for a sample of detailed holdings of British market makers.101 Comparing
the riskiness of the portfolio to various capital requirements, they show
that the net position approach, as required by the United Kingdom, dominates the E.U. and U.S. approaches, as it best approximates the actual
portfolio risk. The net position approach comes closest to what portfolio
theory would suggest.
Although there are differences in the regulations of banks and securities firms, capital requirements are likely to converge as banks and securities firms increasingly compete in the same markets. Currently, the same
accounting rules apply to the trading-book activities of banks and the
trading activities of securities firms. In the United States, the 1933 GlassSteagall Act, which separates the commercial and investment bank functions, is slowly being chipped away. The 1933 act is widely viewed as
obsolete and overly restrictive, especially in comparison with the universal banking system prevalent in Europe. Cracks in the Glass-Steagall wall
started to appear in 1989, when commercial banks were allowed to underwrite stocks and bonds on a limited basis (although no more than 10 percent of their revenues could come from underwriting). Banks have also
been expanding into insurance products, such as annuities, although further expansion is being fiercely resisted by U.S. insurance companies.
More recently, VaR has been gaining prominence in the regulation of
securities firms. The Securities and Exchange Commission, the Commodity Futures Trading Commission, and six major Wall Street securities
houses have entered an agreement to base capital requirements on VaR
methodology. An authoritative resource for counterparty risk management, published by the Counterparty Risk Management Policy Group
(CRMPG) in June 1999, is improving counterparty risk management practices. CRMPG was formed by a group of 12 parties in the aftermath of the
1998 market turmoil to promote better industrywide counterparty market
and credit risk practices. As for the commercial banking system, VaR is
bound to become a universally accepted benchmark.102
2.12.4 The Trend Toward
Risk-Based Disclosures
In addition to deriving strategic benefits from risk measurement and management, institutions can use their risk management systems to generate
the kinds of reports that regulators are seeking. Disclosure guidelines released by the U.S. Securities and Exchange Commission (SEC) in 1997
allow companies to use VaR-type measures to communicate information
about market risk. While many companies may be interested in measuring the aggregate market risk of their underlying exposures and hedge instruments for internal purposes, current regulations require only the
disclosure of market risk–sensitive instruments (e.g., derivative contracts). Disclosure of underlying exposures and other positions is encouraged, but not required. Whether companies decide to report only the
required disclosures or to also include the encouraged disclosures, the
systems being used for internal risk measurement can be leveraged to
meet regulatory disclosure requirements.
2.12.5 Disclosure Requirements
SEC market risk disclosure requirements affect all companies reporting
their financial results in the United States.103 These regulations apply to derivative commodity instruments, derivative financial instruments, and
other financial instruments (investments, loans, structured notes, mortgage-backed securities, indexed debt instruments, interest-only and principal-only obligations, deposits, and other debt obligations) that are sensitive
to market risk, all of which are collectively called market risk–sensitive
The SEC requires that companies provide both quantitative and
qualitative information about the market risk–sensitive instruments they
are using.104 Currently, the allowed alternatives for the reporting of quan-
Market Risk
titative information include tabular summaries of contract fair values;
measures of sensitivity to market rate changes; and VaR measures expressing potential loss of earnings, cash flows, or fair values.
The New Basel Capital Accord has integrated disclosure requirements as an integral part of the entire accord, across all risk factors:
The third pillar, market discipline, will encourage high disclosure standards
and enhance the role of market participants in encouraging banks to hold
adequate capital. The Committee proposes to issue later this year [2001]
guidance on public disclosure that will strengthen the capital framework.105
2.12.6 Encouraged Disclosures
Apart from setting requirements on market risk–sensitive instruments,
the SEC encourages, but does not require, risk disclosures on instruments,
positions, and transactions not covered by Item 305 of Regulation S-K and
Item 9A of Form 20-F. Such instruments can include physically settled
commodity derivatives, commodity positions, cash flows from anticipated transactions, and other financial instruments, such as insurance
contracts. The BIS emphasizes disclosure practices and requires that regulations on the disclosure of specific, relevant information regarding market, credit, and operational risk be enforced; thus, the banks become more
In general, the reporting of the combined market risk of underlying
business exposures and market risk–sensitive instruments should provide
a more accurate portrayal of a firm’s total risk profile than reporting for
market risk–sensitive instruments alone.
Credit exposure and market risk are interrelated, and the boundaries between credit and market risk increasingly overlap and merge; this is particularly obvious in the case of credit risk derivatives. It can be argued that
credit risk is a component of market risk, as it reflects the company- or
issuer-specific risk. A change in the quality of a company and its ability to
fulfill its financial obligations is, in an efficient market, immediately reflected in the specific risk, either on the equity side through the idiosyncratic
risk or on the fixed-income side through the spread on top of the risk-free
term structure. This reflects the balance sheet, as all financing instruments
ultimately lead back to the balance sheet of the original underlying company and should therefore reflect the same company-specific risk.
Credit exposures from market-driven transactions such as swaps,
forwards, and purchased options are an issue for all participants in the
OTC derivatives markets. Credit or market risk can result from fluctuations in market rates. (More instrument types are analyzed and decomposed regarding market, credit, and operational risk in Chapter 3.)
In the case of a swap, the interrelationship of credit and market risk
can be illustrated in a simple example. Party A engages in an interest-rate
swap with Party B, paying a five-year fixed rate and receiving a threemonth LIBOR. If the five-year rate goes down, A incurs a market loss because it agreed to pay B an above-market interest rate. On the other hand, if
a 10-year rate falls, the swap is in the money for A. However, this mark-tomarket (MTM) gain on the swap is now a credit exposure to B—if B defaults,
A forsakes the MTM gain on the swap. Therefore, a company has credit exposure whenever rates fluctuate in its favor. A company has potential credit
exposure from the time a contract is initiated up to final settlement.
For example, simulating a simple equity-index fall would do little to
uncover the risk of a market-neutral risk arbitrage book. In a real-world
example, Long Term Capital Management (LTCM) had leveraged creditspread-tightening positions (i.e., long corporate bond positions were
interest-rate hedged with short Treasuries) in August 1998. This portfolio
was supposedly market neutral.106
A stress test for spread widening (i.e., flight-to-safety phenomenon)
would have uncovered the potential for extreme losses. Stressed markets
often give rise to counterparty credit risk issues that may be much more
significant than pure market impacts. For example, a market-neutral swap
portfolio could result in huge credit exposures if interest rates moved significantly and counterparties defaulted on their contractual obligations.
While market rates and creditworthiness are unrelated for small market
movements, large market movements could precipitate credit events, and
vice versa. Note that it is much more straightforward to reduce market
risk than credit risk. To reduce the market risk in our example, Party A can
purchase a 10-year government bond or futures contract, or enter into an
opposite swap transaction with another counterparty. Credit risk presents
a more complex problem. For example, taking an offsetting swap with another counterparty to reduce market risk actually increases credit risk (one
counterparty will always end up owing the party the net present value of
the swap). Solutions to the credit problem are available, however. Party A
could arrange a credit enhancement structure with Party B, such as structuring a collateral or MTM agreement (e.g., Party B agrees to post collateral or pay the MTM of a swap on a periodic basis, or if a certain threshold
is reached). Furthermore, a credit derivative could be written by a third
party to insure the swap contract.
Options have their own credit and market risk profile (Figure 2-8).
Only purchasers of options have credit exposure to their counterparts. If
the option is in the money and the counterparty defaults, the party is in
trouble. For example, Party A has potential credit exposure when it buys a
Market Risk
F I G U R E 2-8
Market, Credit, and Operational Risks from a Transaction Perspective.
Middle office /
risk control
Risk exposures
put option on the S&P 500 Stock Index to insure an equity portfolio. If the
equity market falls and Party A’s counterparty defaults on its obligation to
honor the put option, A would incur a credit loss (for example, if the insurer of its equity portfolio does not fulfill its obligation). Sellers of options do not have credit exposure. After a party sells an option and collects
the premium, it is not exposed to its counterparty (for example, the counterparty will not owe it anything, but it will potentially owe something to
the counterparty). As a seller of options, a party incurs only market risk
(i.e., the risk that market rates will move out of its favor). The projected
credit exposure of options increases with time, with the peak exposure expected just before final settlement.
The credit risk of swaps and forwards is mostly counterparty risk.
Counterparties engaging in swaps and forwards incur credit exposure to
each other. Swaps and forwards are generally initiated at the money. That
is, at the beginning of a contract, neither counterparty owes the other anything. However, as rates change, the MTM value of the contract changes,
and one counterparty will always owe another counterparty money (the
amount owed will be the MTM value).
Usually, the projected credit exposure of an interest-rate swap has a
concave shape. Projected exposure of a currency swap, however, increases
with time and peaks just before settlement. A currency swap has a larger,
and continually upward sloping, exposure profile due to the foreign-
exchange risk of the principal amount, which is exchanged only at final
settlement. Projected credit exposure of a forward also slopes continually
upward, as there is no exchange of payments before settlement.
Market risk management has become a relatively mature discipline.
Therefore, this chapter focuses on the evolution of the different models and approaches, and on the conditions and assumptions which are
linked to those models and approaches. The groundbreaking works of
Markowitz and Black and Scholes 50 years ago set the framework in the
market risk area, subsequently enhanced and modified by others. These
origins have shaped the profile of the discipline and provided a substantial set of specialized parameters and assumptions, typical for a discipline
considered to have an integrated framework. The terms time horizon, diversification, and volatility, just to mention three parameters, have a different meaning within the market risk framework than in credit risk or
operational risk. The international regulatory body has developed the supervisory framework for each risk category independently from the other
categories, and tries to bring the individual components together in the
new capital adequacy framework.
The discussion of different models and their application within the
regulatory framework covering market risk–related issues is a central part
of this chapter. The Basel Committee on Banking Supervision of the Bank
for International Settlement has moved from a prescriptive approach on
supporting risk with capital to a risk-sensitive framework, and the latest
approach is intended to integrate the market, credit, and operational risk
categories into an integrated risk framework. This chapter focuses on the
conceptual approaches regarding the modeling of market risk and the regulatory initiatives on market risk and VaR.
2.15 NOTES
1. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate Market Risks,
Basel, Switzerland: Bank for International Settlement, January 1996, sec. I.1.
p. 3.
2. Harry M. Markowitz, “Portfolio Selection (1),” Journal of Finance 7 (March
1952), 77–91.
3. William Shakespeare, The Merchant of Venice, ca. 1596–1598, Antonio in act 1,
scene 1.
4. J. R. Hicks, “A Suggestion for Simplifying the Theory of Money,” Economica
(February 1935), 1–19.
5. Ibid., 7.
Market Risk
6. James Tobin, “Liquidity Preference as Behavior Towards Risk,” Review of
Economic Studies 26/1 (February 1958), 65–86.
7. J. R. Hicks, “Liquidity,” Economic Journal 72 (December 1962), 787–802.
8. Ibid.
9. J. Marschak, “Money and the Theory of Assets,” Econometrica 6 (1938),
10. Ibid., 314.
11. James Tobin, “Liquidity Preference as Behavior Towards Risk,” Review of
Economic Studies 26/1 (February 1958), 65–86.
12. William F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium
Under Conditions of Risk,” Journal of Finance 19/3 (September 1964),
425–442; John Lintner, “The Valuation of Risk Assets and the Selection of
Risky Investments in Stock Portfolios and Capital Budgets,” Review of
Economics and Statistics 47/1 (February 1965), 13–37.
13. Johnann von Neumann and Oskar Morgenstern, “Theory of Games and
Economic Behavior,” 3d ed., Princeton, NJ: Princeton University Press, 1967
(1st ed., 1944).
14. J. B. Williams, The Theory of Investment Value, Cambridge, MA: Harvard
University Press, 1938.
15. J. L. Farrell, “The Dividend Discount Model: A Primer,” Financial Analysts
Journal 41 (November–December 1985), 16–19, 22–25.
16. D. H. Leavens, “Diversification of Investments,” Trusts and Estates 80 (May
1945), 469–473.
17. Harry M. Markowitz, “Portfolio Selection (1),” Journal of Finance 7 (March
1952), 77–91.
18. A. D. Roy, “Safety First and the Holding of Assets,” Econometrica 20/3 (July
1952), 431–449.
19. Harry M. Markowitz, “The Optimization of a Quadratic Function Subject to
Linear Constraints,” Naval Research Logistics Quarterly 3 (1956), 111–133;
Portfolio Selection—Efficient Diversification of Investments, New York: John
Wiley & Sons, 1959; Mean-Variance Analysis in Portfolio Choice and Capital
Markets, Oxford, U.K.: Basil Blackwell, 1987.
20. Harry M. Markowitz, Portfolio Selection (2), 2d ed., Oxford, U.K.: Basil
Blackwell, 1992, p. 154ff.
21. James Tobin, “Liquidity Preference as Behavior Towards Risk,” Review of
Economic Studies 26/1 (February 1958), 65–86.
22. William F. Sharpe, “Capital Asset Prices, A Theory of Market Equilibrium
Under Conditions of Risk,” Journal of Finance 19/3 (September 1964),
23. John Lintner, “The Valuation of Risk Assets and the Selection of Risky
Investments in Stock Portfolios and Capital Budgets,” Review of Economics
and Statistics 47/1 (February 1965), 13–37; “Security Prices, Risk, and
Maximal Gains from Diversification,” Journal of Finance 20 (1965), 587–615.
24. Jan Mossin, “Equilibrium in a Capital Asset Market,” Econometrica 35/4
(October 1966), 768–783.
25. Diana R. Harrington, Modern Portfolio Theory, the Capital Asset Pricing Model
and Arbitrage Pricing Theory: A User’s Guide, 2d ed., Englewood Cliffs, NJ:
Prentice-Hall, 1987, p. 35.
26. For a detailed discussion, see Christoph Aukenthaler, “Trust Banking,
Theorie und Praxis des Anlagegeschäftes,” PhD thesis, University of Zurich,
Haupt, Bern, 1991, 244ff., or Pirmin Hotz, “Das Capital Asset Pricing Model
und die Markteffizienzhypothese unter besonderer Berücksichtigung der
empirisch beobachteten ‘Anomalien’ in den amerikanischen und anderen
internationalen Aktienmärkten,” PhD thesis, University St. Gall, Victor Hotz
AG, Baar, 1989, p. 43ff.
27. Eugene Fama, “Efficient Capital Market: A Review of Theory and Empirical
Work,” Journal of Finance 3 (1970), 383–417.
28. Thomas Vock and Heinz Zimmermann, “Risiken und Renditen
schweizerischer Aktien,” Schweizerzische Zeitschrift für Volkwirtschaft und
Statistik 4 (1984), 547–576.
29. Eugene Fama, Foundations of Finance, New York: Basic Books, 1976, p. 25ff.
30. Stanley J. Kon, “Models of Stock Returns—A Comparison,” Journal of Finance
39 (1984), 147–165.
31. Randolph Westerfield, “An Examination of Foreign Exchange Risk and
Fixed and Floating Exchange Rate Regimes,” Journal of International
Economics 7 (1977), 181–200.
32. Walter Wasserfallen and Heinz Zimmermann, “The Behaviour of Interdaily
Exchange Rates,” Journal of Banking and Finance 9 (1985), 55–72.
33. Heinz Zimmermann, “Zeithorizont, Risiko und Performance, eine
Übersicht,” Finanzmarkt und Portfolio Management 2 (1991), 169.
34. Fischer Black, “Capital Market Equilibrium with Restricted Borrowing,”
Journal of Business 7, 444–454.
35. For a detailed analysis see Fischer Black, Michael C. Jensen, and Myron
Scholes, “The Capital Asset Pricing Model: Some Empirical Tests,” in
Michael Jensen, Studies in the Theory of Capital Markets, New York: Praeger,
36. Eugene Fama, “Efficient Capital Market: A Review of Theory and Empirical
Work,” Journal of Finance 3 (1970), 383–417; Fischer Black, Michael C. Jensen,
and Myron Scholes, “The Capital Asset Pricing Model: Some Empirical
Tests,” in Michael Jensen, Studies in the Theory of Capital Markets, New York:
Praeger, 1972; Eugene Fama and James MacBeth, “Risk, Return and
Equilibrium: Empirical Tests,” Journal of Political Economy 9 (1973), 601–636.
37. Stephen A. Ross, “The Arbitrage Theory of Capital Asset Pricing,” Journal of
Economic Theory 13 (1976), 341–360.
38. Louis Bachelier, “Theorie de la Speculation,” Annales de l’Ecole Normale
Superieure 17 (1900), 21–86. English translation by A.J. Boness in Paul H.
Cootner (ed.), The Random Character of Stock Market Prices, Cambridge, MA:
MIT Press, 1967, pp. 17–78.
Market Risk
39. C. Sprenkle, “Warrant Prices as Indicators of Expectations and Preferences,”
Yale Economic Essays 1 (1961), 172–231; P. Samuelson, “Rational Theory of
Warrant Pricing,” Industrial Management Review 10 (1965), 15–31.
40. Fischer Black and Myron Scholes, “The Pricing of Options and Corporate
Liabilities,” Journal of Political Economy 81 (May–June 1973), 637–654; R. C.
Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and
Management Science 4/1 ( June 1974), 141–183.
41. Ibid., Black and Scholes.
42. Ibid., Merton.
43. Fischer Black, “The Pricing of Commodity Contracts,” Journal of Financial
Economics 3 (1976), 167–179.
44. M. Asay, “A Note on the Design of Commodity Option Contracts,” Journal of
Finance 2 (1982), 1–8.
45. M. Garman and S. Kohlhagen, “Foreign Currency Option Values,” Journal of
International Money and Finance 2 (1983), 231–238.
46. R. Geske, “The Valuation of Compound Options,” Journal of Financial
Economics 7 (1979), 63–81.
47. Richard Roll, “An Analytic Valuation Formula for Unprotected American
Call Options on Stocks with Known Dividends,” Journal of Financial
Economics 5 (1977), 251–258; R. Geske, “A Note on an Analytical Formula for
Unprotected American Call Options on Stocks with Known Dividends,”
Journal of Financial Economics 7 (1979), 375–380; R. Whaley, “On the Valuation
of American Call Options on Stocks with Known Dividends,” Journal of
Financial Economics 9 (1981), 207–211.
48. M. Rubinstein, “Pay Now, Choose Later,” Risk (February 1991), 13.
49. S. Gray and R. Whaley, “Valuing S&P 500 Bear Market Warrants with a
Periodic Reset,” Journal of Derivatives 5 (1997), 99–106.
50. B. Goldman, H. Sosin, and M. Gatto, “Path Dependent Options: Buy at the
Low, Sell at the High,” Journal of Finance 34 (1979), 1111–1127.
51. M. Rubinstein and E. Reiner, “Breaking Down the Barriers,” Risk (September
1991), 31–35.
52. J. Cox, S. Ross, and M. Rubinstein, “Option Pricing: A Simplified Approach,”
Journal of Financial Economics 7 (1979), 229–264; R. Rendleman Jr. and B.
Bartter, “Two-State Option Pricing,” Journal of Finance 34 (1979), 1093–1110.
53. P. Boyle, J. Evnine, and S. Gibbs, “Numerical Evaluation of Multivariate
Contingent Claims,” Review of Financial Studies 2 (1989), 241–250.
54. P. Boyle, “A Lattice Framework for Option Pricing with Two State
Variables,” Journal of Financial and Quantitative Analysis 23 (1988), 1–12.
55. E. Schwartz, “The Valuation of Warrants: Implementing a New Approach,”
Journal of Financial Economics 4 (1977), 79–93; M. Brennen and E. Schwartz, “The
Valuation of American Put Options,” Journal of Finance 32 (1977), 449–462.
56. P. Boyle, “Options: A Monte Carlo Approach,” Journal of Financial Economics
4 (1977), 323–338.
57. R. Geske and H. Johnson, “The American Put Valued Analytically,” Journal of
Finance 39 (1984), 1511–1524.
58. G. Barone-Adesi and R. Whaley, “Efficient Analytic Approximation of
American Option Values,” Journal of Finance 42 (1987), 301–320.
59. L. MacMillan, “Analytic Approximation for the American Put Option,”
Advances in Futures and Options Research 1 (1986), 119–139.
60. R. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and
Management Science 4/1 (1973), 141–183.
61. J. Cox and S. Ross, “The Valuation of Options for Alternative Stochastic
Processes,” Journal of Financial Economics 3 (1976), 145–166.
62. E. Derman and I. Kani, “Riding on the Smile,” Risk (July 1994), 32–39;
D. Dupire, “Pricing with a Smile,” Risk (July 1994), 18–20; M. Rubinstein and
E. Reiner, “Implied Binomial Trees,” Journal of Finance 49 (1994), 771–818.
63. R. C. Merton, “Option Pricing when Underlying Stock Returns are
Discontinuous,” Journal of Financial Economics 3 (1976), 125–143.
64. J. Hull and A. White, “The Pricing of Options and Assets with Stochastic
Volatilities,” Journal of Finance 42 (1987), 281–300.
65. L. Scott, “Option Pricing when the Variance Changes Randomly: Theory
Estimation, and an Application,” Journal of Financial and Quantitative Analysis
22 (1987), 419–438; J. Wiggins, “Option Values Under Stochastic Volatility:
Theory and Empirical Estimates,” Journal of Financial Economics 19 (1987),
66. D. Bates, “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit
in PHLX Deutschemark Options,” Review of Financial Studies 9 (1996), 69–108.
67. Alan Greenspan, “Measuring Financial Risk in the Twenty-First Century,”
remarks before a conference sponsored by the Office of the Comptroller of
the Currency, Washington, D.C., October 14, 1999.
68. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, International Convergence of Capital Measurement and Capital
Standards, Basel, Switzerland: Bank for International Settlement, July 1988.
69. See U.S. General Accounting Office, Long-Term Capital Management,
Regulators Need to Focus Greater Attention on Systemic Risk, Washington, DC:
General Accounting Office, October 1999.
70. See the analysis and recommendations in Commodity Futures Trading
Commission (CFTC), Hedge Funds, Leverage, and the Lessons of Long-Term
Capital Management: Report of the President’s Working Group on Financial
Markets, Washington, DC: Commodity Futures Trading Commission, April
1999,, accessed May 19, 2000.
71. Financial Times, “Greenspan Hits Out at Way Banks Treat Risk” (October 12,
1999), 10.
72. The Basel Committee’s members are representatives of the central banks and
local regulatory organizations of the Group of Ten (G-10) countries:
Belgium, Canada, France, Germany, Italy, Japan, the Netherlands, Sweden,
the United Kingdom, and the United States, plus Luxembourg and
Market Risk
Switzerland. The committee meets four times a year, usually in Basel,
Switzerland, under the chairmanship of the Bank for International
Settlement, where the permanent secretariat of the committee is located.
73. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, International Convergence of Capital Measurement and Capital
Standards, Basel, Switzerland: Bank for International Settlement, July 1988.
74. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Prudential Supervision of Banks’ Derivatives Activities, Basel,
Switzerland: Bank for International Settlement, December 1994; Amendment
to the Capital Accord of July 1988, Basel, Switzerland: Bank for International
Settlement, July 1994; Basel Capital Accord: The Treatment of the Credit Risk
Associated with Certain Off-Balance-Sheet Items, Basel, Switzerland: Bank for
International Settlement, July 1994.
75. The U.S. banking industry regulators consist of the Federal Reserve Board,
the Office of the Comptroller of the Currency, and the Federal Deposit
Insurance Corporation.
76. The Basel Committee has extended the add-ons on equities, precious metals,
and commodities contracts and increased the add-ons in general for longer
maturities. See Bank for International Settlement (BIS), Basel Committee on
Banking Supervision, Treatment of Potential Exposure for Off-Balance-Sheet Items,
Basel, Switzerland: Bank for International Settlement, April 1995. See as well
the discussion of the Basel Committee’s 1994 and 1995 modifications in
Section 2.8. See also the regulations issued in Bank for International
Settlement (BIS), Basel Committee on Banking Supervision, Interpretation of the
Capital Accord for the Multilateral Netting of Forward Value Foreign Exchange
Transactions, Basel, Switzerland: Bank for International Settlement, April 1996;
and Survey of Disclosures About Trading and Derivatives Activities of Banks and
Securities Firms: Joint Report by the Basel Committee on Banking Supervision and
the Technical Committee of the International Organisation of Securities Commission,
Basel, Switzerland: Bank for International Settlement, November 1996.
77. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate Market Risks,
Basel, Switzerland: Bank for International Settlement, January 1996,
modified in September 1997.
78. Ibid.
79. Committee members who are also members of the European Union regard
this definition as being consistent with (albeit less detailed than) the
definition of the trading book in the EU’s Capital Adequacy Directive.
80. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate Market Risks,
Basel, Switzerland: Bank for International Settlement, January 1996,
modified September 1997.
81. Ibid., para. II.a.
82. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, The New Basel Capital Accord: Consultative Document, Issued for
Comment by 31 May 2001, Basel, Switzerland: Bank for International
Settlement, January 2001, part 2I, para. 20.
83. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate Market Risks,
Basel, Switzerland: Bank for International Settlement, January 1996,
modified September 1997, para. 7.
84. Switzerland Federal Banking Commission, “Guidelines Governing Capital
Adequacy Requirements to Support Market Risks,” EG-FBC Circular No.
97/1, October 22, 1997.
85. See comments in Reto R. Gallati, “De-Minimis-Regel diskriminiert,”
Schweizer Bank (Zurich), 9 (1998), 41–43.
86. See definition of specific risk in Bank for International Settlement (BIS),
Basel Committee on Banking Supervision, Amendment to the Capital Accord to
Incorporate Market Risks, Basel, Switzerland: Bank for International
Settlement, January 1996, modified September 1997, para. I.b, footnote 5.
87. See Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, International Convergence of Capital Measurement and Capital
Standards, Basel, Switzerland: Bank for International Settlement, July 1988.
88. Traded mortgage securities and mortgage derivative products possess
unique characteristics because of the risk of prepayment. Accordingly, for
the time being, no common treatment applies to these securities, which are
dealt with at national discretion. A security that is the subject of a
repurchase or securities-lending agreement will be treated as if it were still
owned by the lender of the security—i.e., it will be treated in the same
manner as other securities positions.
89. This includes the delta-equivalent value of options. The delta equivalent of
the legs arising out of the treatment of caps and floors can also be offset
against each other under the rules laid down in this paragraph.
90. The separate legs of different swaps may also be matched, subject to the
same conditions.
91. Where equities are part of a forward contract, a future, or an option
(quantity of equities to be received or to be delivered), any interest rate or
foreign currency exposure from the other leg of the contract should be
92. For example, an equity swap, in which a bank receives an amount based on
the change in value of one particular equity or stock index, and pays on a
different index will be treated as a long position in the former and a short
position in the latter. Where one of the legs involves receiving or paying a
fixed or floating interest rate, that exposure should be slotted into the
appropriate repricing time band for interest-rate-related instruments. The
stock index should be covered by the equity treatment.
93. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate Market Risks,
Basel, Switzerland: Bank for International Settlement, January 1996,
modified September 1997, sec. 5.3.1, para. 130.
Market Risk
94. Ibid., sec. 5.3.2.b, para. 96.
95. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Proposal to Issue a Supplement to the Basel Capital Accord to Cover
Market Risks, Basel, Switzerland: Bank for International Settlement, April
1995; An Internal Model–Based Approach to Market Risk Capital Requirements,
Basel, Switzerland: Bank for International Settlement, 1995.
96. Alan Greenspan, “Risk Management in the Global Financial System—Before
the Annual Financial Markets Conference of the Federal Reserve Bank of
Atlanta,” Miami Beach, Florida, February 27, 1998.
97. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Supervisory Framework for the Use of “Backtesting” in Conjunction
with the Internal Models Approach to Market Risk Capital Requirements, Basel,
Switzerland: Bank for International Settlement, January 1996.
98. P. Kupiec and J. O’Brien, “A Pre-Commitment Approach to Capital
Requirements for Market Risk,” FEDS Working Paper no. 95-34,
Washington, DC: Federal Reserve Board of Governors, 1995.
99. A typical management response is to cut positions as losses accumulate.
This pattern of trading can be compared to portfolio insurance, which
attempts to replicate a put option. Therefore, attempts by management to
control losses will create a pattern of payoffs over long horizons that will be
asymmetrical, similar to options. The problem is that traditional VaR
measures are inadequate with highly nonlinear payoffs.
100. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, The New Basel Capital Accord: Consultative Document, Issued for
Comment by 31 May 2001, Basel, Switzerland: Bank for International
Settlement, January 2001, 6ff.; Amendment to the Capital Accord to Incorporate
Market Risks, Basel, Switzerland: Bank for International Settlement, January
1996, modified September 1997.
101. E. Dimson and R. Marsh, “Capital Requirements for Securities Firms,”
Journal of Finance 50 (1995), 821–851.
102. Misconceptions of models are that they are conceptually built for “normal
conditions”. See comments from Tim Shepheard-Walwyn and Robert
Litterman, “Building a Coherent Risk Measurement and Capital
Optimization Model for Financial Firms,” paper presented at the
Conference on Financial Services at the Crossroads: Capital Regulation in
the 21st Century, New York, February 26–27, 1998, FRBNY Economic Policy
Review (October 1998), 173ff. and Section 5.8 of this book, which discusses
misconceptions of models.
103. See Securities and Exchange Commission Item 305 of Regulation S-K and
Item 9A of Form 20-F.
104. For a description of the required qualitative market risk disclosures, see
Securities and Exchange Commission Item 305(b) of Regulation S-K and
Item 9A(b) of Form 20-F.
105. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, The New Basel Capital Accord: Consultative Document, Issued for
Comment by 31 May 2001, Basel, Switzerland: Bank for International
Settlement, January 2001, paras. 74, 655ff.
106. A market-neutral risk arbitrage book would consist of a series of long and
short positions; this hedges out market risk but leaves exposure to firmspecific risk. A trading strategy that eliminates broad market risk (equity,
interest rate, foreign exchange, or commodity) leaves only residual risk. For
example, a hedge fund manager can hedge the market risk of a U.S. stock
portfolio by shorting S&P 500 Stock Index futures, leaving only firm-specific
residual risk.
Credit Risk
Over the past decade, a number of the world’s largest banks and research and academic institutions have developed sophisticated systems
that model the credit risk arising from important aspects of their businesses. Such systems have been designed for identifying, quantifying, aggregating, and managing credit risk exposures. The output and analysis of
these systems have become increasingly important in risk management,
performance measurement (including performance-oriented compensation), and customer profitability analysis, as well as in forming the base
for decisions in credit portfolio management and for equity-capital allocation by the institution.
These systems and models are used for internal purposes by those
who manage credit risks, and they also have the potential to be used in the
supervisory oversight of the entire organization. The authorization of the
modeling approach to be used in the formal process of setting regulatory
capital requirements for credit risks depends on several conditions. Regulators have to be confident that the models are used to actively manage
risk, that the models are conceptually sound and empirically validated,
and that the procedures for capital requirements are adequate and comparable across institutions. The major concerns are data integrity and
availability and validation of the conceptual model.
The following paragraphs discuss the different approaches to credit
risk management, including how economic and regulatory conditions and
assumptions are congruent. The increase of structured products that have
simultaneous credit risk and market risk components has to be taken into
account when designing such models.
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This work uses the definition of credit risk contained in a 1996 report of the
Bank for International Settlement (BIS):1
Credit risk/exposure: the risk that a counterparty will not settle an obligation for full value, either when due or at any time thereafter. In exchangefor-value systems, the risk is generally defined to include replacement risk
and principal risk.
This work also uses a consistent definition of loan:2
A “loan” is a financial asset resulting from the delivery of cash or other assets by a lender to a borrower in return for an obligation to repay on a specified date or dates, or on demand, usually with interest.
Loans include the following:
Consumer installments, overdrafts and credit card loans
Residential mortgages
Nonpersonal loans, such as commercial mortgages, project
finance loans, and loans to businesses, financial institutions,
governments, and their agencies
Direct financing leases
Other financing arrangements that are, in substance, loans
Loan impairment represents deterioration in the credit quality of one
or more loans such that it is probable that the bank will be unable to collect, or there is no longer reasonable assurance that the bank will be able
to collect, all amounts due according to the contractual terms of the loan
Current credit risk regulations are based on the 1988 BIS guidelines. These
minimum requirements have been subsequently enforced and implemented by local regulators at the national level by more than 100 nations,
and they include minimum standards for capital adequacy for credit risks
and the definition of the countable equity capital. Since 1988 the regulations
have been modified five times, primarily during the transitional period of
1988 to 1992.4 In 1989 the regulations were materially modified by substantially differentiating capital requirements for balance and off-balance positions, and by extending the incorporation of subordinated loans to the
equity calculation. Based on the BIS guidelines, the calculation approach
was switched to the indirect capital requirement calculation method in
1994. Balance sheet positions are first weighted according to their relative
counterparty risk and then multiplied by the standard capital requirement
of 8 percent. The basic problem with this approach is that securitization and
Credit Risk
other forms of capital arbitrage allow banks to achieve effective capital requirements well below the nominal 8 percent Basel standard.
The regulatory risk weights do not reflect certain risks, such as interestrate and operating risks. More important, they ignore critical differences in
credit risk among financial instruments (for example, all commercial credits
incur a 100 percent risk weight), as well as differences across banks in hedging, portfolio diversification, and the quality of risk management systems.
These anomalies create opportunities for “regulatory capital arbitrage” that
render the formal risk-based capital ratios increasingly less meaningful for
the largest, most sophisticated banks. Through securitization and other financial innovations, many large banks have lowered their risk-based capital
requirements substantially without reducing materially their overall credit
risk exposures. More recently, the September 1997 Market Risk Amendment
to the Basel Accord created additional arbitrage opportunities by affording
certain credit risk positions much lower risk-based capital requirements
when held in the trading account rather than in the banking book.
Despite several substantial modifications, the current framework for
capital requirements does not reflect the fact that market and risk management have evolved over the past 10 years (see Figure 3-1). The BIS has
published a consultative paper on reform of its 1998 capital accord.5
The fundamental concept of the capital accord is relatively simple—it assumes that for all banks, independent of their size, business activity, and
level of development of risk management, only one standardized approach exists, which contains several defects. The original accord focused
mainly on credit risk; it has since been amended to address market risk.
Interest-rate risk in the banking book and other risks, such as operational,
liquidity, legal, and reputational risks, are not explicitly addressed:
The risk weightings for counterparties are not differentiated in
detail and thus do not represent the risk in an adequate and
sensitive form.
Correlations between the positions in a credit portfolio are not
considered. A risk reducing diversification from a portfolio
management approach is not rewarded with lower capital
requirements. An individual credit position of $50 million is
treated in the same way as a portfolio of five different credits of
$10 million each.
The current regulations do not consider hedging of credit risk
positions with credit derivatives. Offsetting positions that
economically net out each have to be supported with capital.
F I G U R E 3-1
Trend of Risk Management Sophistication and Capital Adequacy Regulation.
Consideration of:
• Current credit risk regulation as set by BIS
• Current enhancement through netting /
offsetting agreements as set by BIS
Consideration of:
• Individual risk rating and thus risk
• Different duration (time buckets) for
individual securities
• Netting / offsetting agreement
• Credit derivatives
Capital adequacy requirements
Current credit risk regulation
Consideration of:
• Correlation resulting in diversification
• Integrated, consistent risk measurement
• Netting / offsetting agreement
• Credit derivatives
Simplified (standard) approach
Credit risk model approach
Risk management sophistication
Credit Risk
Convergence from capital markets to commercial lending drive
risk analytics, e.g., credit securitization, credit derivatives, and
option-pricing models.
The following factors challenge credit risk management and must be
included in the discussion to develop a useful credit risk methodology:
The current practice does not distinguish between transaction
and portfolio approaches. These approaches represent different
levels in the credit process and must be integrated together.
Commercial loans are often complex heterogeneous contracts
with a number of complicated embedded options and other
structural elements.
Measuring risk-adjusted profitability is difficult due to a lack of
good understanding of “true” operating and economic capital costs.
Due to limited loan trading, a market view of loan value is hard
to come by, making it cumbersome to compare value between
loans and other traded asset classes.
The existing credit risk models use a conceptual setup similar to that for the
measurement of market risks. Most market risk models have evolved from
a mean-variance approach and developed further, as the profit-and-loss
(P&L) distribution did not fit the assumptions of the models. For market
risks, a variety of different approaches are used to calculate P&L distributions: the RiskMetrics approach, historical simulation, and Monte Carlo
simulation. Delta-gamma methods have been developed to identify and
adjust distributions for the nonlinear component of risk.6 The regulatory
requirements can be better covered with an insurance or actuarial approach, which uses econometric methods such as autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) and
scenario analysis and historical databases reaching back a long time to analyze and calculate these extreme events.
The existing commercial credit risk models are based on the concept of
covering losses with adequate pricing and provisions. This is basically a cost
approach applied to a portfolio of credit positions, whereas the regulatory
approach is more of a loss approach implemented to identify and measure
individual extreme events and to calculate the loss from such events.
To calculate the default probability, the ratings for the borrowers’
positions are needed. Data availability and data integrity generally dictate
the methods used to estimate expected default frequency (EDF)/transition matrices. At most banks, internal credit ratings are a key variable—or
in some cases the sole criterion—for assigning borrowers to risk segments.
This is especially true with large corporate credit customers. Most banks
have stored historical aggregate performance data by broad loan types or
lines of business, but not by risk grade. Furthermore, such databases generally go back only a few years, at best.
Since banks typically have comparatively little useful internal default and migration data, they often attempt to estimate EDF/transition
matrices using historical performance studies published by the rating
agencies, such as Standard & Poor’s, Moody’s or Duff & Phelps. Such historical data often reports historical default, loss, and rating migration experience by rating category, covering time spans of 20 or more years.
However, in some cases, the geographical and industry composition of
this published data may not be appropriate to the characteristics of the
loan portfolio being modeled. For example, published rating agency data
is often dominated by U.S. experience and based on U.S. accounting practices. Using inappropriate transition matrices will result in misleading
assessments of credit risk.7 External rating information is sometimes adjusted based on judgment to incorporate internal information on the borrower’s creditability. To use an experience database for credits, a bank
must first develop or assume some economic and econometric relations
between the internal rating categories and the grading systems applied by
the rating agencies. Such correspondences are commonly developed
using four basic approaches, either individually or in combination:
The first approach involves matching historical default
frequencies within each internal rating grade to the default
frequencies by the agency’s rating category.
The second approach compares a bank’s own internal grades with
those of the rating agencies for borrowers that are rated by both.
Such comparisons may not be possible for major segments of the
portfolio (middle-market customers, non-U.S. business firms).
The third method attempts to expand the population of firms for
which such comparisons are possible by constructing
pseudo–credit agency ratings for firms not formally rated by the
agencies. This is accomplished by estimating the relationship
between agency ratings and financial and other characteristics of
firms using publicly available data for agency-rated firms.
The fourth approach involves subjective comparison of the
bank’s rating criteria for assigning internal grades with the rating
agencies’ published rating criteria.
Unlike the market risk approach, backtesting is not yet seriously applicable. The methodology applied to backtesting market risk value-atrisk (VaR) models is not easily transferable to credit risk models due to the
Credit Risk
data constraints. The market risk amendment requires a minimum of 250
trading days of forecasts and realized losses. A similar standard for credit
risk models would require an impractical number of years of data, given
the models’ longer time horizons. Given the limited availability of data for
out-of-sample testing, backtesting estimates of unexpected credit loss is
certain to be problematic in practice, as previously mentioned. Where
analyses of ex-ante estimates and ex-post experience are made, banks typically compare the historical time series of estimated credit risk losses to
historical series of current credit losses captured over some years. However, the comparison of expected and actual credit losses does not address
the accuracy of the model’s forecasting ability of unexpected losses,
against which economic capital is allocated. While such independent
work on backtesting is limited, some literature indicates the difficulty of
ensuring that capital requirements generated using credit risk models will
provide an adequately large capital buffer.8
However, the assumption underlying these approaches is that prevailing market perceptions of credit spreads (for rate-of-return analysis)
are substantially accurate and economically well founded. If this is not so,
reliance on such techniques raises questions as to the comparability and
consistency of credit risk models, an issue which may be of particular importance to supervisors.9
The design of the credit risk management structure and culture varies
from bank to bank. While some banks have implemented systems and
structures that measure and monitor credit risk exposures throughout the
organization, other institutions have structures that monitor credit risk exposures within given business lines or legal entities. In addition, some
banks have separate models for corporate and retail clients.
The internal applications of model output also span a wide range,
from the simple to the complex. The trend is increasing, but a few organizations still use the output for active credit portfolio management. The
current applications include setting concentration and limit exposures,
risk-based pricing, evaluation of the risk-return profile of business lines or
portfolio managers using risk-adjusted return on capital (RAROC), and
calculation of economic capital calculation for the different business lines.
Institutions also rely on model estimates for setting or validating loan loss
reserves, either for direct calculations or for validation purposes.
These models have some factors, conditions, and assumptions in
common which must be analyzed in more detailed. When possible, it is
best to bring all these factors and parameters to their highest common denominator.
The most critical factors of the different conceptual approaches to credit
risk modeling are the following:
Probability density function of credit loss
Expected and unexpected credit loss
Time horizon
Default mode
Conditional versus unconditional models
Approaches to credit risk aggregation
Correlations between credit events.
There are five main factors contributing to the level of credit risk losses
with credit risk models:
Changes in loss rate given defaults
Rating migrations
Correlations among default and rating transitions
Changes in credit spreads
Changes in exposure levels
3.6.1 Transaction and Portfolio Management
Transaction and portfolio management serve complementary objectives:
Transaction management pursues value creation.
Portfolio management pursues value preservation.
Transaction management is based on individual transaction optimization and added value through the use of appropriate risk and
pricing models, methods for structuring loan instruments, and the like
for individual positions. Relationships to other segments and markets
are not included in this view. The portfolio management approach
considers all factors (such as correlations, volatilities, etc.) for a portfolio in order to optimize and preserve the existing risk-return level in
a portfolio.
Depending on the credit risk management setup, different activities
(such as securitization, credit derivatives, syndicated loans, etc.) are possible with the given infrastructure and management know-how. Figure 3-2
gives an overview of the impact of the loan structure on credit risk management decisions.
Depending on the credit risk management type, the focus is on different objectives. At the transaction level, the focus is on:
Measuring credit risk using risk ratings and default and loss
probability calculations
Credit Risk
F I G U R E 3-2
Impact of Loan Structure on Credit Risk Management Approach.
"Back end"
"Front end"
Transaction management
Underwrite /
originate new
Portfolio management
hold / sell
Credit structure and embedded optionalities impact is significant on approach to credit risk management
Developing and using migration models
Integrating risk ratings into the credit process.
The key input elements are risk ratings. Risk-rating methodology is
developed with three objectives in mind:
Measure credit risk (default and loss probability or potential)
using good discrimination, separation, and accuracy across the
full spectrum of credit risk.
Provide management with accurate and meaningful information
for decision making.
Produce supportable and accurate information for regulatory and
financial statement reporting purposes. Primary Approaches to Risk Rating
Table 3-1 gives an overview of the primary approaches. Migration Models
Migration models can help to calibrate the risk rating and the predicted
losses by default frequency and amount of loss. The objectives are as
Adjust the internal rating process to external rating systems.
Support provisioning requirements.
Determine the risk cost by rating.
Support risk-based pricing.
T A B L E 3-1
Overview of Primary Approaches to Risk Rating
Judgmental approach/
expert systems
Relationship managers
and/or credit officers
assign ratings based on
financial ratios, opinions
on management quality,
and other data collected
in due diligence review;
expert system codifies
rules of successful loan
Subjective; ratings affected
by fads or politics;
vulnerable to relativity
and anchoring; no
numerical estimates of
risk term structures
except by reference to
past experience.
In-place common,
historical track record
may be available; allows
for nonquantitative factors;
promotes identification of
risk factors.
Most bank systems
Discriminant analysis
Classifies companies or
facilities into several
categories based on
financial ratios measuring
leverage, debt-service
coverage, volatility; uses
historical default data to
calibrate model.
Oriented to the history;
often calibrated over an
arbitrary period; usually no
term structure; prone to
Simple to apply to all
borrowers, allows testing
of many variables and
functional forms.
Altman’s Z score
Contingent claims
(options model)
Capital owners hold a
default option, which
they exercise when
advantageous; associated
with migration model;
predicts cumulative default
probabilities as a function
of market leverage,
term, and volatility.
Oriented to the future;
parsimonious; determines
default term structure;
measures sensitivity to
changing business
Hard to apply and
probably less reliable for
private firms; unbundling
of volatility of structured
and securitized products
to identify risk factors.
KMV’s CreditMonitor
Credit Risk
F I G U R E 3-3
Average Loss Rate Approach for Measuring Rating Transitions.
3 Period average loss rate
4 Period average loss rate
2 Period average loss rate
1 Period average loss rate
Cumulative losses, %
Time horizon
The average loss rate model measures transactional losses by risk rating.
The cumulative loss over several periods is calculated on the basis of individual positions allocated to credit development curves, which are based
on average loss rates based on historical experience. Figure 3-3 shows the
development curves for two positions.
Applying a Markov approach, the model measures rating transitions
through various “credit” stages (see Figure 3-4). The true Markov process
probabilities are based on the following assumptions:
F I G U R E 3-4
Markov Process for Measuring Rating Transitions.
Grade 1
Grade 1
Grade 1
Grade 2
Grade 2
Transitional state
Grade 3
Grade 3
Loss %
Absorbing state
Loss %
The model is independent of its prior grade history.
The model is constant over time.
The probabilities are the same for all credits in a given category
regardless of the specific credit characteristics.
The probabilities are independent of the movements of other credits.
The results from the Markov process have to be mapped against
standard ratings (e.g., from S&P) to review and calibrate the internal
process to external rating information (see Figure 3-5).
The EDF is an essential input for many analytical methodologies and
models, including risk-based pricing, RAROC, and quantitative models
(e.g., CreditMetrics). EDFs also allow financial institutions to test the alignment of their own grading systems across different business units and
against third-party data. (See comments on EDF in Section
3.6.2 Measuring Transaction
Risk–Adjusted Profitability
The current performance measurement approaches use two different
methodologies: RAROC and net present value (NPV). Performance
measurement comes in many variations. The statements in Table 3-2
F I G U R E 3-5
Mapping of the Markov Process to External Rating Information.
risk rating
Markov transition matrix — EDF
Grade 1
Grade 1
Grade 1
Grade 1
AAA to
Grade 2
Grade 2
Grade 2
A+ to A-
Grade 3
Grade 3
Grade 3
BBB+ to
Grade n
Grade n
Grade n
BBB- to
BB to BB-
Time horizon t
Credit Risk
T A B L E 3-2
Comparison of Current Performance Measurement Approaches
Can treat credit risk as dynamic
Tends to take a static view of credit risk
Can value embedded optionalities
and credit structure
Typically does not consider credit structure
and optionalities
Can calibrate to the market or to an
internal risk premium
Tends to be policy driven and accounting
Can consider credit risk migrations
in multistate framework
Tends to be two-state
refer to the way in which most transaction-level RAROC models are
Credit portfolio management requires the following:
Rich data and informational resources
A structure that spans multiple organizations and functions
A consistent organizational vision that promotes concerted action
To calculate a portfolio VaR, multiple input information is required:
Ratings transition probabilities
Correlations across borrowers
Information on the pricing and structure of each loan position
and contract:
Loan type (revolving versus term)
Spread and fees
Options (e.g., prepayment,
repricing or grid, and term-out)
In general, a portfolio model and a transaction model must be integrated
in order to deliver useful output information.
Economic Capital Allocation Probability Density Function of Credit Losses
Sophisticated financial organizations use an analytical setup that relates the
overall required economic capital of the institute to its credit activities.
The required economic capital is linked to the portfolio’s credit risk with the
probability density function (PDF) of credit losses, a key result from the credit
risk model.10 An important element is the probability that credit losses will
exceed a given amount, which is represented by the area under the density
function to the right of the given limit (the upper limit covering expected
credit losses). A portfolio with a higher risk of credit loss is one whose density under the function has a relatively long and fat tail (see Figure 3-6).
The expected credit loss is defined as the total amount of credit losses
the bank would expect from its credit portfolio over a specific time horizon (leftmost vertical line in Figure 3-6). The expected loss is one of the
costs of transacting business that gives rise to credit risk. For marketing
and other reasons, financial institutes prefer to express the risk of the
credit portfolio by the unexpected credit loss, i.e., the amount by which the
actual losses exceed the expected loss. The unexpected loss is a measure of
the uncertainty or variability of actual losses versus expected losses. The
estimated economic capital needed to support the institution’s credit portfolio activities is generally referred to as its required economic capital for
credit risk. A cushion of economic capital is required for loss absorption,
F I G U R E 3-6
Probability Density Function (PDF) of Credit Losses.
Expected credit loss
Allocated economic capital
99% confidence level
1% loss
Extreme credit losses — tail events
Covered by
adequate pricing
and loss
Covered by loss provisions and/or
proprietary capital
Covered by loss provisions and/or
proprietary capital quantified using
scenario analysis and controlled with
concentration limits
Credit Risk
because the actual level of credit losses suffered in any one period could
be significantly higher than the expected level. The procedure for calculating this amount is similar to the VaR methods used in allocating economic capital for market risks. The understanding is that economic capital
for credit risk is determined in such a way that the estimated probability
of unexpected credit loss exhausting economic capital is less than some
target insolvency rate.
The capital allocation systems generally assume that it is the role of
reserve funding to cover expected credit losses, while it is the role of economic capital to cover unexpected credit losses. The required economic
capital represents the additional amount of capital necessary to achieve
the target insolvency rate, over and above that needed for coverage of expected losses (the distance between the two lines in Figure 3-6). Measuring Credit Loss
Loss in a credit portfolio is defined by three variables: the difference between the portfolio’s current value and its future value at the end of a certain
time horizon. Because many functions depend on the time dimension in
one way or another, the time horizon is a key input variable for the definition of risk. There are basically two ways of selecting the time horizon
over which credit risk is monitored:
The first approach is the application of a standardized time period
across all contracts (instruments). Most financial institutions
adopt a one-year time horizon across all asset classes (not only
credit instruments).
The second is the liquidation period approach, in which each
credit contract (instrument) is associated with a unique time
period, coinciding with the instrument’s maturity or with the
time needed for liquidation. Some vendor systems allow
specific time periods for asset classes or portfolios (for
structured credit portfolios). The hold-to-maturity approach
seems to be applicable if the exposures were intended to be held
to maturity and/or liquid markets for trading these instruments
are limited.
The factors influencing the fixing of the period are as follows:
Availability or publication of default information
Availability of borrower information
Internal control rhythms and renewal processes
Capital planning
Account statement preparations; changes to the capital structure
(capital increase or reduction).
144 Default-Mode Paradigm
The default-mode (DM) paradigm states that a credit loss occurs only if a
borrower defaults on a repayment obligation within the planning horizon.
As long as the default event does not become a fact, no credit loss would
exist. In the event that the borrower defaults on obligations, the credit loss
is calculated as the difference between the bank’s credit exposure (the
amount due to the bank at the moment of default) and the present value
of future net recoveries (discounted cash flows from the borrower less
workout expenses). The current and the future values of the credit are defined in the default-mode paradigm based on the underlying two-state
(default versus nondefault) notion of the credit loss. The current value is
typically calculated as the bank’s credit exposure (e.g., book value). The
future value of the loan is uncertain. It would depend on whether the borrower defaults during the defined time horizon. In the case of nondefault,
the credit’s future value is calculated as the bank’s credit engagement at
the end of the time horizon (adjusted so as to add back any principal payments made over the time horizon).
In the case of a default, the future value of the credit is calculated as
the credit minus loss rate given default (LGD). The higher the recovery rate
following default, the lower the LGD. Using a credit risk model, the current value of the credit instrument is assumed to be known, but the future
value is uncertain. Applying a default-mode credit risk model for each individual credit contract (e.g., loan versus commitment versus counterparty risk), the financial institution must define or estimate the joint
probability distribution between all credit contracts with respect to three
types of random variables:
The bank’s associated credit exposure
A binary zero/one indicator denoting whether the credit contract
defaults during the defined time horizon
In the event of default, the associated LGD Mark-to-Market Paradigm
The mark-to-market (MTM) paradigm treats all credit contracts under the
assumption that a credit loss can arise over time, deteriorating the asset’s
credit quality before the end of the planned time horizon. The mark-tomarket paradigm treats all credit contracts as instruments of a portfolio
being marked to market (or, more accurately, marked to model) at the beginning and end of the defined time horizon. The credit loss reflects the
difference of the valuation at the beginning and at the end of the time horizon. This approach considers changes in the asset’s creditworthiness, reflecting events that occur before the end of the time horizon. These models
must incorporate the probabilities of credit rating migrations (through the
rating transition matrix), reflecting the changes in creditworthiness.
Credit Risk
For each credit position in the portfolio, migration paths have to be
calculated, using the rating transition matrix and Monte Carlo simulation.
For all positions, the simulated migration (including the risk premium associated with the contract’s rating grade at the end of the rating period) is
used to mark the position to market (or, more accurately, to model) as of
the end of the time horizon. For the purpose of estimating the current and
future values of the credit contracts, two approaches can be used:
The discounted contractual cash flow (DCCF) approach
The risk-neutral valuation (RNV) approach Discounted Contractual Cash Flow Approach
The discounted contractual cash flow (DCCF) approach is commonly associated with J. P. Morgan’s CreditMetrics methodology. The current value of
a nondefaulted loan is calculated as the present discounted value of its future contractual cash flows. For a credit contract with an assigned risk rating (i.e., BBB), the credit spreads used for the calculation of the discounted
cash flows of the credit contract equal the market-determined term structure of credit spreads corresponding to similar corporate bonds (maturity,
coupon, sinking-fund provision, etc.) with that same rating. The current
value is treated as known, because the future value of the credit depends
on the (uncertain) end-of-period rating and the market-determined term
structure of credit spreads associated with the specific rating. The future
value of the credit is subject to changes in migration (creditworthiness) or
in the credit spreads according to the market-determined term structure.
In the event of default, the future value of a credit would be given by its
recovery value, calculated as the credit minus loss rate given default (a
similar approach to that used in the default-mode approach).
The DCCF approach is a practical approach, but it is not completely in
line with modern finance theory. For all contracts with the same rating, the
same discount rates are assigned. Thus, for all contracts not defaulted within
the defined time horizon, the future value does not depend on the expected
loss rate given default, as they are not defaulted. Modern finance theory
holds that the value of an asset (borrower’s asset) depends on the correlation
of its return with that of the market. Borrowers in different market segments,
exposed to different business cycles and other risk factors, will still be assigned to the same risk grade according to the DCCF approach. Risk-Neutral Valuation Approach
To avoid the pitfalls of the discounted contractual cash flow approach,
Robert Merton developed a structural approach imposing a model of firm
value and bankruptcy.11 A company defaults when the value of its underlying assets falls beneath the level required to serve its debt. The riskneutral valuation (RNV) approach discounts contingent payments instead
of discounting contractual payments. A credit can be considered as a set of
derivative contracts on the underlying value of the borrower’s assets. If a
payment (interest rate, amortization, etc.) is contractually due at date t, the
payment actually received by the lender will be the contractual amount
only if the firm has not defaulted by date t. The lender receives a portion of
the credit’s face amount equal to the credit minus loss rate given default
(an approach similar to that used in the default-mode method) if the borrower defaults at date t, and the lender receives nothing at date t if the borrower has defaulted prior to date t. The value of the credit equals the sum
of the present values of these derivative contracts (each payment obligation at time t is regarded as an option). The difference from the discount
rates used for the discounted contractual cash flow approach is that the discount rate applied to the contracts’ contingent cash flows is determined
using a risk-free term structure of interest rates and the risk-neutral pricing
measure. Similar to the option-adjusted spread approach, the risk-neutral
pricing measure can be regarded as an adjustment to the probabilities of
borrower default at each horizon t, which incorporates the market risk premium associated with the borrower’s default risk. The magnitude of the
adjustment depends on the expected return and volatility of the borrower’s asset value. Returns modeled consistently with the capital asset
pricing model (CAPM) can be expressed in terms of the market expected
return and the firm’s correlation beta (β) with the market. This approach
combines pricing of the credits with the respective credit losses:
The expected default frequency and the loss rate given default by
the borrower
The correlation between the borrower’s risk and the systematic
(market) risk
This is consistent with modern finance theory.
The interpretation of default is key in understanding the risk-neutral
valuation approach. A credit is considered to be in default once it migrates
to a predefined limit. This worst-case scenario is not clearly defined; it
varies according to the institution’s risk appetite and risk capacity, thus affecting measures of default, migration, credit loss, and the probability
density function.
Choice of Time Horizon
As mentioned earlier, most institutions use a one-year time horizon to
measure their credit risk exposures. This has to do more with computational convenience and availability of information rather than with internal process and model optimization. The definition of default used in
credit models is not congruent with that applied for legal purposes. The
institution may consider a credit to be in default if the credit is classified as
Credit Risk
falling below an investment-grade rating, if cash flows are past due, if the
credit is placed on a nonaccrual status, if recovery proceedings are initiated, and so forth.
The time horizon appears to be an important variable for the assessment of capacity of models to meet economic and regulatory needs.
The ability of a default-mode model to assess the effects of potentially unfavorable credit events due to the model’s two-state nature (i.e.,
default/nondefault) may be particularly sensitive to the defined length of
the time horizon.
Credit Loss Measurement Definition DM Versus MTM Models
Both the default-mode (DM) and mark-to-market (MTM) approaches estimate the credit losses from adverse changes in credit quality. The quality
of credit models is primarily influenced by the fit between the model output and the model application. The model choice should be made based
on the circumstances of the use and application. An institution that uses a
portfolio of liquid credits and exposure to credit spreads (i.e., the hedge
transactions for credit portfolios using credit spreads between different
term structures) may require a credit loss measurement definition that incorporates potential shifts in credit spreads and thus opt for the (more
complicated) MTM model with the multistate nature. DCCF Versus RNV Approaches
In practice, the difference between the approaches is smaller than in theory,
because the credit value is priced as a discounted present value of its future
cash flows in both approaches. The dichotomy is sharper in theory because
the discount factors are calculated differently. The discounted contractual
cash flow (DCCF) approach assumes a nonparametric approach to estimating these discount factors. The public debt issuers (issues) are grouped
into rating categories, and the credit spreads on the issuers are then averaged within each rating “bucket.” On the other hand, the risk-neutral valuation (RNV) approach is more complex. In a structural process, each
credit is simultaneously modeled in an individual framework. This means
that the modeling of the market risk premium for each credit in the RNV
model is typically referenced to credit spreads from the debt market.
The empirical evidence of the econometric theory shows that highly
structural estimators make efficient use of available data but are vulnerable to model misspecification. Nonparametric estimators make minimal
use of modeling assumptions but underperform where data integrity is a
problem. The two approaches will, in general, assign different credit
losses to any given loan. Under normal market conditions (liquidity and
information efficiency) and the stable assumptions of the RNV model,
both approaches should deliver reasonable output for a well-diversified
credit portfolio.
The probability that a particular credit contract will default during the
time horizon is a critical input. The bank’s credit staff has to assign internal
credit risk ratings for all credit contracts. This is done for most corporate
customers. The trend is that all customers, corporate or retail, are assigned
risk ratings in order to obtain the overall risk profile of the credit portfolio,
including the correlations between the different segments of the portfolio as
they are exposed to different business cycles, macroeconomic factors, etc.
There are basically three approaches (which can be combined) for assigning a credit rating to a customer or the contract:
The traditional approach, based on financial, accounting, and
other characteristics of the customer. This approach is very
subjective and is based on the reliability and availability of
specific information.
Credit-scoring models supplied by commercial vendors, which
also deliver a database that reflects the best-practice standards in
the market.
Credit-scoring models developed internally, which reflect the
structure and the processes of the credit department.
External ratings are frequently combined with internal rating categories, which allows combination of the internal credit authorization
process and external rating data. The expected default frequency (EDF) can
be interpreted as a credit’s probability of migrating from its current internal rating grade to default within the credit model’s time horizon. The likelihood of such a migration from its current risk rating category to another
category is defined in the transition matrix, as illustrated in Table 3-3.
Given the contract’s actual rating (defined by each row), the probability to migrate to another category (defined by the columns) is defined
within the intersecting cell of the transition matrix. Thus, in Table 3-3, the
likelihood of a credit contract rated A migrating to BBB within one year
would be 7.4 percent. The likelihood of a credit contract rated CCC migrating to default within one year would be 18.6 percent. Unconditional Versus Conditional Models
In a broad sense, all models are conditional, as they process input information on the credit quality of the borrower and the credit contracts. In a
narrower sense, it is possible to distinguish between unconditional and
conditional models. The unconditional models process information limited to the borrower and the credit contracts. The transition matrix and the
correlations are modeled to capture the long-run values of these parameters. But such long-run averages may misrepresent the short-term condition, as correlations and default frequency tend to vary systematically
Credit Risk
T A B L E 3-3
Sample Credit Rating Transition Matrix: Probability of Migrating
to Another Rating Within 1 Year
Rating at Year End, %
SOURCE: Greg M. Gupton, Christopher C. Finger, and Mickey Bhatia, CreditMetrics Technical Document, New York: Morgan
Guaranty Trust Co., April 1997, 76. Copyright © 1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with
permission of RiskMetrics Group, Inc.
with the course of the business cycle. The conditional models process information on the borrower and the credit contracts and, in addition, are
linked to macroeconomic information such as gross domestic product,
current levels and trends in domestic and international employment, inflation rates, indicators specific for particular sectors, etc.
CreditMetrics and CreditRisk are examples of unconditional risk models. They estimate the expected default frequency and correlations between
historical default data and borrower- or contract-specific information, such
as the rating. These models are based on data collected and estimated over
many credit cycles to reflect the averages of these parameters. They should
predict reasonable credit loss probabilities based on the transition matrix, if
the credit portfolio is composed of similar credit contracts. This type of
model has drawbacks; if the borrowers are upgraded or downgraded over
time, their expected default rates will be revised downward or upward.
Such a portfolio will not have a similar standard deviation over time and
will be more complex to manage relative to given risk levels. The unconditional models are not able to incorporate macroeconomic parameters such
as business cycle effects. The tendency for rating improvement or deterioration is positive during cyclical upturns or downturns, respectively.
The drawbacks of the unconditional models are avoided with the conditional models. Examples of conditional credit risk models include McKinsey and Company’s CreditPortfolioView12 and KMV’s PortfolioManager.
Within its conceptual modeling, the transition matrices of CreditPortfolioView are related to the state of the economy, as the matrices of the covariance matrix are modified to give an increased likelihood of an upgrade (and
decreased likelihood of a downgrade) during an upswing (or downswing)
in a credit cycle. KMV’s PortfolioManager links the process of estimating
the asset values, rates of return, and volatility to current equity prices,
which are information-efficient and incorporate all information available in
the market. This approach is comparable to the arbitrage price theory (APT)
and the multifactor models. Empirical research has generated empirical evidence. The drawbacks of these models are timing and parameterization.
They might underestimate losses as the credit cycle enters a downturn and
overestimate losses as the cycle bottoms out.
3.7.4 Risk Aggregation
Within most credit risk approaches, broadly similar conceptual approaches
are implemented, modeling individual-level credit risk exposures for different type of positions. Most banks measure credit risk at the individual
asset level for capital market and corporate instruments (bottom-up approach), while aggregate data is used for quantifying risk for different types
of positions (top-down approach), including product lines such as consumer,
credit card, or mortgage portfolios.
Bottom-up approaches attempt to measure credit risk at the
individual level of each facility based on an explicit evaluation of
the creditworthiness of the portfolio’s constituent debtors. Each
specific position in the portfolio is linked with an individual risk
rating, typically used as a proxy for the EDF or the probability of
rating migration.13 The data is then aggregated to the portfolio
level, taking into account diversification effects based on the
correlation matrix.
Top-down approaches are used to cope with the sheer number of
exposures. Typically, for retail positions, a top-down empirical
approach is applied. The information for individual positions is
allocated to specific factors and aggregated into buckets, such as
credit scores, age, geographical location, collateralized exposures,
and so forth. The credit risk is quantified at the level of these
buckets. Facilities within each bucket are treated as statistically
identical. In the process of estimating the distribution of credit
losses, the model builder would attempt to model both the
aggregate default rate and the LGD rate using historical time-series
data for that risk segment (bucket) taken as a whole, rather than by
arriving at this average through a joint consideration of default and
migration risk factors for each specific facility in the pool.
Credit Risk
The literature on credit risk models tends to make a distinction between these two approaches, whereas in practice the differences are less
clear-cut. The differences in the implementation arise primarily in the ways
the underlying parameters are estimated using the available data. The distinction between top-down and bottom-up approaches is not always precise. The key consideration is the degree to which a financial institution can
distinguish meaningfully between borrower classes (buckets). Frequently,
so-called bottom-up models rely on aggregate data to estimate individual
borrower parameters. A practical example is the mapping of individual borrower ratings (a bottom-up approach) to a transition matrix calculated from
pooled data, which is derived from published ratings by rating agencies or
from internal statistics (an average of aggregate top-down data). The accuracy of aggregate data and the compatibility to the financial institution’s actual credit portfolio influences the use of aggregate data and potentially
distorts idiosyncratic loan-specific effects to which the financial institution
is exposed.
3.8.1 Background
Over the past few years, a revolution has been brewing in the way credit
risk is both measured and managed. In contrast to the accounting-driven,
relatively dull, and routine history of credit risk, new technologies and
methodologies have emerged among a new generation of financial engineering professionals who are applying their engineering skills and
analysis to this risk topic.
Why is this development happening now? The eight most obvious
reasons for this sudden surge in interest are as follows:
Maturing market risk area. Given the maturity of market risk
models, the experience gained over the past decades, based on
theoretical and academic research and practical experience which
has relativized and improved the relevance of market risk
modeling, the market risk area has evolved in a way that frees
resources and welcomes new challenges, such as credit and
operational risk.
Disintermediation of borrowers. As capital markets have expanded
and become accessible to small- and middle-market firms,
borrowers left behind to raise funds from banks and other
traditional financial institutions are increasingly likely to be
smaller and have weaker credit ratings. Capital market growth
has produced a “winner’s curse” effect on the credit portfolio
structure of traditional financial institutions.
Competitive margin structure. Almost paradoxically, despite a
decline in the average quality of loans (due to disintermediation),
the respective margin spreads, especially in wholesale loan
markets, have become very thin—that is, the risk–premium
trade-off from lending has gotten worse. A number of reasons can
be cited, but an important factor is the enhanced competition for
lower-quality borrowers, such as from finance companies, much
of whose lending activity is concentrated at the higher-risk,
lower-quality end of the market.
Structural change in bankruptcies. Although the most recent
recessions hit at different times in different countries, most
bankruptcy statistics showed a significant increase in
bankruptcies, compared to the prior economic downsides. To the
extent that there has been a permanent or structural increase in
bankruptcies worldwide—possibly due to the increase in global
competition and sectoral changes, such as the technology
sector—accurate credit risk analysis becomes even more
important today than in the past.
Diminishing and volatile values of collaterals. Concurrent with the
ongoing Asian crisis, banking crises in well-developed countries
have shown that real estate values and precise asset values are
very hard to predict and to realize through liquidation. The
weaker the rating and the more uncertain collateral values are,
the more risky lending is likely to be.
Exposures from off-balance-sheet derivatives. The growth of credit
exposure and counterparty risk, based on the phenomenal
growth of the derivative markets, has extended the need for
credit analysis beyond the loan book. In many of the largest
banks, the notional (not market) value of the off-balance-sheet
exposure to instruments such as over-the-counter (OTC) swaps
and forwards exceeds more than 10 times the size of the loan
portfolios. The growth in credit risk off the balance sheet was one
of the reasons for the introduction of risk-based capital
requirements in 1993.14
Capital requirements. Under the BIS system, banks have to hold a
capital requirement based on the marked-to-market current value
of each OTC derivatives contract (so-called current exposure)
plus an add-on for potential future exposure.
Technological advances. Computer infrastructure developments
and related advances in information technology—such as the
development of historic information databases—have given
banks and financial organizations the opportunity to test highpowered modeling techniques. In the case of credit risk
Credit Risk
management, besides being able to analyze loan loss and value
distribution functions and especially the tails distributions,
the infrastructure enables the active management of loan
portfolios, based on modern portfolio theory (MPT) models
and techniques.15
3.8.2 BIS Risk-Based Capital
Requirement Framework
Despite the importance of the reasons previously discussed, probably the
greatest incentive and key impetus to the development of enhanced credit
risk models has been dissatisfaction with the BIS and local regulators’ imposition of capital requirements on loans. The current BIS regime has been
described as a “one size fits all” policy; virtually all loans to private-sector
counterparties are subjected to the same 8 percent capital ratio (or capital
reserve requirement), not taking into account the different impacts of the
size of the loan; the maturity of the loan; or, most important, the credit
quality (rating) of the borrowing counterparty. Under current capital requirement terms, loans to a firm near bankruptcy are treated in the same
fashion as loans to a AAA borrower or the government. Further, the current capital requirement is additive across all loans; there is no allowance
for lower capital requirements because of a greater degree of diversification in the loan portfolio.
In 1997, the European Community was the first to give certain large
banks the discretion to calculate capital requirements for their trading
books—or market risk exposures—using internal models rather than the alternative regulatory (standardized) model. Internal models are subject to
certain constraints imposed by regulators and are subjected to backtesting
verification.16 They potentially allow the following revisions:
VaR of each tradable instrument to be more accurately measured
(e.g., based on its price volatility, maturity, etc.)
Correlations among assets (diversification effect) to be taken into
In the context of market risk, VaR is defined as the predicted worstcase loss at a specific confidence level (e.g., 95 percent) over a certain period of time (e.g., 10 days). For example, under the BIS market risk
regulations, when banks calculate their VaR-based capital requirements
using their internal models, they are required to measure the worst-case
day as the worst day that happens once every 100 business days. The current regulative framework is additive and does not consider diversification in the loan portfolio to allow lower capital requirements.
The critical questions for bankers and regulators developing a new
framework are the following:
Can an internal-model approach be used to measure the VaR or
capital exposure of (nontradable) loans?
Do internal models provide sufficient flexibility and accuracy to
support the standardized 8 percent risk-based capital ratio that
imposes the same capital requirement on virtually all privatesector loans?
Internal models require additional enhancements before they can replace the 8 percent rule, especially because of the nontradability of some
types of loans compared to marketable instruments, and the lack of deep historic databases on loan defaults. However, the new internal models offer
added value to financial organizations, regulators, and risk managers. Specifically, internal model approaches potentially offer better insight on how to
value and manage outstanding loans and credit risk–exposed instruments
such as bonds (corporate and emerging market), as well as better methods for
estimating default risk probabilities regarding borrowers and derivative
counterparties. Moreover, internal models have the following advantages:
In many cases they allow a better estimation of the credit risk of
portfolios of loans and credit risk–sensitive instruments.
They enhance the pricing of new loans, in the context of a bank’s
RAROC, and of relatively new instruments in the credit
derivatives markets (such as credit options, credit swaps, and
credit forwards). The models provide an alternative opportunity
to measure the optimal or economic amount of capital a bank
should hold as part of its capital structure.
Before looking at some of these models and new approaches to credit
risk measurement, a brief analysis of the more traditional approaches will
heighten the contrast between the new and traditional approaches to
credit risk measurement.
3.8.3 Traditional Credit Risk
Measurement Approaches Background
It is hard to draw a clear line between traditional and new approaches, as
many of the superior concepts of the traditional models are used in the
new models. For the purposes of this historical review, the traditional
credit models are segregated into three types: expert systems, rating systems, and credit-scoring systems.17 Expert Systems
In an expert system, the credit decision is made by the local or branch
credit officer. Implicitly, this person’s expertise, skill set, subjective judg-
Credit Risk
ment, and weighting of certain key factors are the most important determinants in the decision to grant credit. The potential factors and expert
systems a credit officer could look at are infinite. However, one of the most
common expert systems, the “five Cs” of credit, will yield sufficient understanding. The expert analyzes these five key factors, subjectively
weights them, and reaches a credit decision:
Capital structure. The equity-to-debt ratio (leverage) is viewed
as a good predictor of bankruptcy probability. High leverage
suggests greater probability of bankruptcy than low leverage, as a
low level of equity reduces the ability of the business to survive
losses of income.
Capacity. The ability to repay debts reflects the volatility of the
borrower’s earnings. If repayments on debt contracts proves to be
a constant stream over time, but earnings are volatile (and thus
have a high standard deviation), the probability is high that the
firm’s capacity to repay debt claims is at risk.
Collateral. In the event of a default, a lender has a claim on the
collateral pledged by the borrower. The greater the proportion of
this claim and the greater the market value of the underlying
collateral, the lower the remaining exposure risk of the loan in the
case of a default.
Cycle/economic conditions. An important factor in determining
credit risk exposure is the state of the business cycle, especially
for cycle-dependent industries. For example, the infrastructure
sectors (such as the metal industries, construction, etc.) tend to be
more cycle dependent than nondurable goods sectors, such as
food, retail, and services. Similarly, industries that have exposure
to international competitive conditions tend to be cycle sensitive.
Taylor, in an analysis of Dun and Bradstreet bankruptcy data by
industry (both means and standard deviations), found some quite
dramatic differences in U.S. industry failure rates during the
business cycle.18
Character. This is a measure of the firm’s reputation, its
willingness to repay, and its credit history. In particular, it has
been established empirically that the age factor of an organization
is a good proxy for its repayment reputation.
Another factor, not covered by the five Cs, is the interest rate. It
is well known from economic theory that the relationship between the
interest-rate level and the expected return on a loan (loss probability) is
highly nonlinear.19 At low interest-rate levels, the expected return could increase if rates are raised. However, at high interest-rate levels, an increase
in rates may lower the return on a loan, as the probability of loss increases.
This negative relationship between high loan rates and expected loan returns is due to two effects: (1) adverse selection and (2) risk shifting. When
loan rates rise beyond some point, good borrowers drop out of the loan
market, preferring to self-finance their investment projects or to seek
equity capital funding (adverse selection). The remaining borrowers, who
have limited liability and limited equity at stake—and thus lower ratings—have the incentive to shift into riskier projects (risk shifting). In upside economies and supporting conditions, they will be able to repay their
debts to the bank. If economic conditions weaken, they will have limited
downside loss from a borrower’s perspective.
Although many financial institutions still use expert systems as part
of their credit decision process, these systems face two main problems regarding the decision process:
Consistency. What are the important common factors to analyze
across different types of groups of borrowers?
Subjectivity. What are the optimal weights to apply to the factors
In principle, the subjective weights applied to the five Cs derived by an expert can vary from borrower to borrower. This makes comparability of
rankings and decisions across the loan portfolio very difficult for an individual attempting to monitor a personal decision and for other experts in
general. As a result, quite different processes and standards can be applied
within a financial organization to similar types of borrowers. It can be argued that the supervising committees or multilayered signature authorities
are key mechanisms in avoiding consistency problems and subjectivity, but
it is unclear how effectively they impose common standards in practice.20 Rating Systems
One of the oldest rating systems for loans was developed by the U.S. Office of the Comptroller of the Currency (OCC). The system has been used
in the United States by regulators and bankers to assess the adequacy of
their loan loss reserves. The OCC rating system allocates an existing loan
into five rating buckets: four low-quality ratings and one high-quality rating. In Table 3-4, the required loss reserve appears next to each category.
Over the years, the financial institutions have extended and enhanced the OCC-based rating system by developing internal rating systems that more finely subdivide the pass/performing rating category.
The OCC pass grade is divided into six different categories (ratings
1 to 6). Ratings 7 to 10 correspond to the OCC’s four low-quality loan ratings. These loan-rating systems do not exactly correspond with the bondrating systems, especially at the lower-quality end of the spectrum (see
Section for a further discussion of bond-rating systems). One reason is the different focus of the approaches: loan-rating systems are sup-
Credit Risk
T A B L E 3-4
Example for Loss Reserves Based on Rating System
Rating Bucket
Loss Reserves, %
Low-quality ratings
Other assets especially mentioned (OAEM)
Substandard assets
Doubtful assets
Loss assets
High-quality rating
NOTE: From a technical perspective, the 0 percent loss reserves for OAEM and pass loans are lower bounds. In practice,
the reserve rates on these categories are determined by the bank in consultation with examiners and auditors, depending
on some type of historical analysis of charge-off rates for the bank.
U.S. Office of the Comptroller of the Currency, EC-159 (rev.), December 10, 1979,
posed to rate an individual loan (including its covenants and collateral
backing). Bond-rating systems are more oriented toward rating the overall borrower. This gap of one-to-one mapping between bond and loan rating methodologies raises a flag as to the merits of those newer approaches
that rely on bond data (spreads, transition matrices, etc.) to value and
price loans individually and in a portfolio context.
Given this trend toward finer internal ratings of loans, compared to
the OCC’s regulatory model, the 1998 Federal Reserve System Task Force
Report21 and Mingo22 give some tentative support for using an internal
model ratings-based approach as an alternative to the OCC model, to calculate capital reserves against unexpected losses, and loan loss reserves
against expected loan losses. For example, using the outstanding dollar
value of loans in each internal rating class (1 to 10), a bank might calculate
its capital requirement against unexpected loan losses as follows:
total class 1 loans ⋅ 0.2%
Capital requirement =
total class 10 loans ⋅ 100%
The 0.2 percent for rating class 1 is just suggestive of unexpected loss
rates and should be based on historic loss probabilities of a loan in class 1
moving to class 10 (loss) over the next year.23 However, an important prob-
lem remains, similar to the current 8 percent risk-based capital ratio of the
BIS approach—the diversification in the loan portfolio is not considered.
The credit risks of each rating class are simply added up to calculate a total
capital requirement. Credit-Scoring Systems
Credit-scoring approaches can be found in virtually all types of credit
analysis. The basic concept is generally the same: certain key factors are
preidentified. They determine the loss probability of default and the recovery rate (as opposed to repayment), and they are combined or weighted
into a quantitative score schema. The score can be literally interpreted as a
loss probability of default. In other scoring systems, the score can be regarded as a classification system: it allocates a potential or existing borrower into either a good group (higher rating) or a bad group (lower
rating), based on a score and a cutoff point. Full reviews of the traditional
approach to credit scoring, and the various methodologies, can be found in
Caouette, Altman, and Narayanan24 and in Saunders.25 See Altman and
Narayanan for a good review of the worldwide application of creditscoring models.26 One simple example of this new credit risk model type
should cover the key issues supposedly addressed by many of these newer
models. The Altman Z-score model is a classification model for corporate
borrowers and can also be used to get a default probability prediction.27
Based on a matched sample by year, size, and sectors of defaulted and solvent firms, and applying the linear discriminant analysis, the best-fitting
scoring model for commercial loans results in the following equation:
Z = 1.2 ⋅ X1 + 1.4 ⋅ X2 + 3.3 ⋅ X3 + 0.6 ⋅ X4 + 1.0 ⋅ X5
where X1 = working capital/total assets ratio
X2 = retained earnings/total assets ratio
X3 = earnings before interest and taxes/total assets ratio
X4 = market value of equity/book value of total liabilities ratio
X5 = sales/total assets ratio
If a corporate borrower’s accounting ratios Xi, weighted by the estimated coefficients in the Z function, result in a Z score below a critical
value (in Altman’s initial study, 1.81), the borrower would be classified as
“insufficient” and the loan would be refused.
A number of issues need to be discussed here. First, the model is linear, whereas the path to bankruptcy can be assumed to be highly nonlinear, and the relationship between the Xi values itself is likely to be
nonlinear. A second issue is that, with the exception of the market value of
equity term in the leverage ratio, the model is essentially based on accounting ratios. In most countries, standards require accounting data only
Credit Risk
at discrete intervals (e.g., quarterly) and are generally based on historic- or
book-value accounting principles. It is also questionable whether such
models can capture the momentum of a firm whose condition is rapidly
deteriorating (e.g., as in the Russia crisis of October 1998). As the world
becomes more complex and competitive, and the decision flow becomes
faster, the predictability of simple Z-score models may worsen. Brazil offers a good example. When fitted in the mid-1970s, the Z-score model did
a quite good job of predicting default even two or three years prior to
bankruptcy.28 However, more recently, even with low inflation and greater
economic stability, this type of model has performed less well as the
Brazilian economy has become more open.29
The recent application of nonlinear methods (such as neural networks) to credit risk analysis shows potential to improve on the proven
credit-scoring models. Rather than assuming there is only a linear and direct effect from the Xi variables on the Z credit score (or, in the language of
neural networks, from the input layer to the output layer), neural networks allow for additional explanatory power via complex correlations or
interactions among the Xi variables (many of which are nonlinear). For example, the five variables in the Altman Z-score model can be described by
some nonlinearly transformed sum of X1 and X2 as a further explanatory
variable.30 In neural network terminology, the complex correlations
among the Xi variables form a “hidden layer” which, when exploited (i.e.,
included in the model), can improve the fit and reduce type 1 and type 2
errors. (A type 1 error consists of misjudging a bad loan as good; a type 2
error consists of misjudging a good loan as bad.)
Yet, neural networks pose many problems for financial economists.
How many additional hidden correlations should be included? In the
language of neural networks, when should training stop? It is entirely
possible that a large neural network, including large N nonlinear transformations of sums of the Xi variables, can reduce type 1 and type 2 errors
of a historic loan database close to zero. However, as is well known, this
creates the problem of overfitting—a model that well explains in-sample
data may perform quite poorly in predicting out-of-sample data. More
generally, the issue is when does one stop adding variables—when the remaining forecasting error is reduced to 10 percent, 5 percent, or less? Reality might prove that what is thought to be a global minimum forecast
error may turn out to be just a local minimum. In general, the issue of economic meaning is probably the most troubling aspect of financial interpretation and use. For example, what is the economic meaning of an
exponentially transformed sum of the GARCH-adjusted sales to total assets and the credit-spread-adjusted discount factor ratio? The ad hoc economic nature of these models and their tenuous links to existing financial
theory separate them from some of the newer models that are discussed
in the following chapters.
3.8.4 Option Theory, Credit Risk, and the KMV Model Background
The idea of applying option pricing theory to the valuation of risky loans
and bonds has been in the literature at least as far back as Merton.31 In recent years, Merton’s approach has been extended in many directions. KMV
Corporation’s CreditMonitor model, a default prediction model that produces (and updates) default predictions for all major companies and banks
whose equity is publicly traded, is one well-known and widely applied option theory–based loan valuation model.32 This section explains the link between loans and options, then investigates how this link can be used to
derive a default prediction model. (Option theory is discussed in more detail in Section 2.4.5.) Loans as Options
Figure 3-7 demonstrates the link between loans and optionality. Assume
that this represents a one-year loan and the amount OB is borrowed on a
discount basis. Technically, option formulas model loans as zero-coupon
bonds with fixed maturities. Over the year, the borrowing firm will invest
the funds in various investments or assets. Assuming that at the end of the
year the market value of the borrowing firm’s assets is OA2 , the borrower
has an incentive to repay the loan (OB) and keep the residual as profit or return on investment (OA2 − OB). Indeed, for any value of the firm’s assets exceeding OB, the owners of the firm will have an incentive to repay the loan.
However, if the market value of the firm’s assets is less than OB (e.g., OA1 in
Figure 3-7), the owners have an incentive (or option) to default and to turn
over the remaining assets of the firm to the lender (the bank).
F I G U R E 3-7
Payoff $
Link Between Loans and Optionality.
Credit Risk
For market values of assets exceeding OB, the bank will earn a fixed upside return on the loan; essentially, interest and principal will be repaid in full.
For asset values less than OB, the bank suffers increasingly large losses. In the
extreme case, the bank’s payoff is zero: principal and interest are a total loss.33
The loan payoff function shown in Figure 3-7—a fixed payoff on the
upside and a long-tailed downside risk—looks familiar to an option theorist. Comparing this profile with the payoff profile of a short put option on
a stock (shown in Figure 3-8) makes the correspondence more obvious. If
the price of the stock S exceeds the strike price K, the writer of the option
will keep the put premium received. If the price of the stock falls below K,
the writer will lose successively larger amounts.
Merton noted this formal payoff equivalence; that is, if a bank grants
a loan, its payoff is isomorphic to short a put option on the assets of the borrowing firm.34 Moreover, just five variables enter the classic Black-ScholesMerton model of a put option valuation for stocks (equity capital); the
value of the default option (or, more generally, the value of a risky loan)
will also depend on and reflect on the value of five similar variables.
In general form:
Value of a put option on a stock = f(S,K,r,T,σS)
Value of a default option on a risky loan = f(E
where S, K, E, and B are as previously defined (a bar above a variable denotes that it is not directly observable); r is the short-term interest rate; E
and σE are, respectively, the volatilities of the firm’s equity value and the
market value of its assets; and r is the maturity of the put option or, in the
case of loans, the time horizon (default horizon) for the loan.
F I G U R E 3-8
Payoff Profile of a Written Put Option on a Stock.
Payoff $
Stock price S
In general, for options on stocks, all five variables on the right-hand
side of Equation (3.3) are directly observable; however, this is true for only
three variables on the right-hand side of Equation (3.4). The market value
of a firm’s assets E and the volatility of the market value of a firm’s assets
σE are not directly observable. If E and σE could be directly measured, the
value of a risky loan, the value of the default option, and the equilibrium
spread on a risky loan over the risk-free rate could all be calculated.35
Some analysts have substituted the observed market value of risky
debt on the left-hand side of Equation (3.4) (or, where appropriate, the observed interest spread between a firm’s risky bonds and a matched riskfree Treasury rate) and have assumed that the book value of assets equals
the market value of assets. This allows the implied volatility of assets σE to
be backed out from Equation (3.4).36 However, without additional assumptions, it is impossible to input two unobservable values (E and σE),
based solely on one equation [Equation (3.4)]. Moreover, the market value
of risky corporate debt is hard to get for all but a few firms.37 Corporate
bond price information is generally not easily available to the public, and
quoted bond prices are often artificial matrix prices.37 KMV CreditMonitor Model
The innovation of the KMV CreditMonitor model is that it looks at the
bank’s lending problem from the viewpoint of the borrowing firm’s equity holders and considers the loan repayment incentive problem (see bibliography). To solve the two unknown variables, E and σE, the system uses
the following relationships:
The structural relationship between the market value of a firm’s
equity and the market value of its assets.
The relationship between the volatility of a firm’s assets and the
volatility of a firm’s equity. After values of these variables are
derived, an expected default frequency (EDF) measure for the
borrower can be calculated.
Figure 3-9 shows the loan repayment issue from the side of the borrower (the equity owner of the borrowing firm). Suppose the firm borrows
OB and the end-of-period market value of the firm’s assets is OA2 (where
OA2 > OB). The firm will then repay the loan, and the equity owners will
keep the residual value of the firm’s assets (OA2 − OB). The larger the market value of the firm’s assets at the end of the loan period, the greater the
residual value of the firm’s assets to the equity holders (borrowers). However, if the firm’s assets fall below OB (e.g., are equal to OA1), the borrowers
of the firm will not be able to repay the loan.39 They will be economically insolvent, will declare bankruptcy, and will turn the firm’s assets over to the
bank. Note that the downside risk to the equity owners is truncated no matter how low asset values are, compared to the amount borrowed. Specifi-
Credit Risk
F I G U R E 3-9
Value of equity E, $
Call Option to Replicate the Equity of a Firm.
Amount OB
Amount OA2
Value of assets A
cally, “limited liability” protects the equity owners against losing more than
OL (the owners’ original stake in the firm). As shown in Figure 3-9, the payoff to the equity holder of a leveraged firm has a limited downside and a
long-tailed upside. Being familiar with options, we recognize the similarity
between the payoff function of an equity owner in a leveraged firm and
buying a call option on a stock. Thus, we can view the market-value position of equity holders in a borrowing firm E as isomorphic to holding a call
option on the assets of the firm A.
In general terms; equity can be valued as:
E = h(A
苶, 苶
In Equation (3.5), the observed market value of a borrowing firm’s
equity (price of shares × number of shares) depends on the same five variables as in Equation (3.4), as per the Black-Scholes-Merton model for valuing a call option (on the assets of a firm). However, a problem still remains:
how to solve two unknowns (A and σA) from one equation (where E, r, B,
and T are all observable).
KMV and others in the literature have resolved this problem by noting that a second relationship can be exploited: the theoretical relationship
between the observable volatility of a firm’s equity value σ E苶 and the unobservable volatility of a firm’s asset value σA. In general terms:
苶E = g(σA)
With two equations and two unknowns, Equations (3.5) and (3.6) can
be used to derive a solution for A and σA by successive iteration. Explicit
functional forms for the option-pricing model (OPM) in Equation (3.5) and
for the stock price–asset volatility linkage in Equation (3.6) have to be specified.40 KMV uses an option-pricing Black-Scholes-Merton-type model that
allows for dividends. B, the default exercise point, is taken as the value of
all short-term liabilities (one year and under), plus half the book value of
outstanding long-term debt. While the KMV model uses a framework similar to that of Black-Scholes-Merton, the actual model implemented, which
KMV calls the Vasicek-Kealhofer model, makes a number of changes in order
to produce usable results. These modifications include defining five classes
of liabilities, reflecting cash payouts such as dividends, handling convertible debt, assuming the default point is an absorbing barrier, and relying on
an empirical distribution to convert distance to default into a default probability. The precise strike price or default boundary has varied under different generations of the model. There is a question as to whether net
short-term liabilities should be used instead of total short-term liabilities.41
The maturity variable t can also be altered according to the default horizon
of the analyst; it is most commonly set equal to one year. A slightly different OPM was used by Ronn and Verma to solve a very similar problem, estimating the default risk of U.S. banks.42
After they have been calculated, the A and σA values can be employed, along with assumptions about the values of B and T, to generate a
theoretically based EDF score for any given borrower.
The idea is shown in Figure 3-10. Suppose that the values backed out
of Equations (3.5) and (3.6) for any given borrower are, respectively, A =
F I G U R E 3-10
Theoretical EDF and Default Loss Region
+ σA
- σA
A = $100 M
Default region
B = $80 M
Time t
Credit Risk
$100 million and σA = $10 million, where σA is the annual standard deviation of the asset value. The value of B is $80 million. In practice, the user
can set the default boundary or exercise price B equal to any proportion of
total debt outstanding that is of interest. Suppose we want to calculate the
EDF for a one-year horizon. Given the values of A, σA, B, and r, and with r
equal to one year, what is the theoretical probability of a borrowing firm’s
failure at the one-year horizon? As can be seen in Figure 3-10, the EDF is
the cross-hatched area of the distribution of asset values below B. This
area represents the probability that the current value of the firm’s assets,
$100 million, will drop below $80 million at the one-year time horizon.
If it is assumed that future asset values are normally distributed
around the firm’s current asset value, we can measure the t = 0 (or today’s)
distance from default at the one-year horizon as follows:
A − B $100 M − $80 M
Distance from default = ᎏᎏ = ᎏᎏ
$10 M
= 2 standard deviations
For the firm to enter the default region (the shaded area), asset values
would have to drop by $20 million, or 2 standard deviations, during the
next year. If asset values are normally distributed, we know that there is a
95 percent probability that asset values will vary between plus and minus
2σ from their mean value. Thus, there is a 2.5 percent probability that asset
values will increase by more than 2σ over the next year, and a 2.5 percent
probability that they will fall by more than 2σ. In other words, there is an
EDF of 2.5 percent. We have shown no growth in expected or mean asset
values over the one-year period in Figure 3-10, but this can easily be incorporated. For example, if we project that the value of the firm’s assets
will grow 10 percent over the next year, then the relevant EDF would be
lower because asset values would have to drop by 3σ, which is below the
firm’s expected asset growth path, for the firm to default at year-end. The
distance from default is:43
A(1 + g) − B $110 M − $80 M
ᎏᎏ = ᎏᎏ = 3 standard deviations
$10 M
The normal distribution assumption of asset values around some
mean level is critical in calculating joint default transition probabilities in
J. P. Morgan’s CreditMetrics (see Section, yet there is an important
issue as to whether it is theoretically or empirically reasonable to make
this assumption. With this in mind, rather than producing theoretical
EDFs, the KMV approach generates an empirical EDF along the following lines. Suppose that we have a large historic database of firm defaults
and no defaults (repayments), and we calculate that the firm we are analyzing has a theoretical distance from default of 2σ. We then ask the empirical questions:
What percentage of the borrowers in the database actually
defaulted within the one-year time horizon when their asset
values placed them a distance of 2σ away from default at the
beginning of the year?
What is the percentage of the total population of borrowers that
were 2σ away from default at the beginning of the year?
This produces an empirical EDF:
Empirical EDF =
Number of borrowers that defaulted
within a year with asset values of 2σ
from B at the beginning of the year
Total population of borrowers with
asset values of 2σ from B at the
beginning of the year
Assume that, based on a global database, it was estimated that 5 percent of all possible firms defaulted. As a result, this empirically based EDF
can differ quite significantly from the theoretically based EDF. From a proprietary perspective, KMV’s advantage comes from building up a large
global database of firms (and firm defaults) that can produce such empirically based EDF scores.
The EDFs have a tendency to rise before the credit quality deterioration is reflected in the agency ratings. This greater sensitivity of EDF
scores, compared to both accounting-based and rating-based systems,
comes from the direct link between EDF scores and stock market prices.
As new information about a borrower is generated, its stock price and
stock price volatility will react, as will its implied asset value A and standard deviation of asset value σA.44 Changes in A and σA generate changes
in EDFs. For actively traded firms, it would be possible (in theory) to update an EDF every few minutes. In actuality, KMV can update EDF scores
frequently for some 20,000 firms globally.
Because an EDF score reflects information signals transmitted from
equity markets, it might be argued that the model is likely to work best in
highly efficient equity market conditions and might not work well in
many emerging markets. This argument ignores the fact that many thinly
traded stocks are those of relatively closely held companies. Thus, major
trades by insiders, such as sales of large blocks of shares (and thus major
movements in a firm’s stock price), may carry powerful signals about the
future prospects of a borrowing firm.
Credit Risk
Overall, the option-pricing approach to bankruptcy prediction has a
number of strengths. It can be applied to any public company. Further, because it is based on stock market data rather than historic book value accounting data, it is forward-looking. In addition, it has a strong theoretical
framework, because it is a structural model based on the modern theory of
corporate finance and options, in which equity is viewed as a call option on
the assets of a firm. However, the strengths can be offset by four weaknesses:
Construction of theoretical EDFs is difficult without the
assumption of normality of asset returns.
It does not differentiate between different types of long-term
bonds according to their seniority, collateral, covenants, or
The private firms’ EDFs can be estimated only by using some
comparability analysis based on accounting data and other
observable characteristics of the borrower and thus are subject to
the same criticisms regarding subjectivity and consistency as are
the expert systems.
It is static in that the Merton model assumes that once
management puts a debt structure in place, it leaves this structure
unchanged even if the value of a firm’s assets has increased or
decreased substantially. As a result, the Merton model cannot
capture the financial behavior of those firms that seek to maintain
a constant or target leverage ratio (debt to equity) across time.45 Structural and Intensity-Based Models
An additional potential problem with KMV-type models, and the BlackScholes-Merton structural model approach on which they are based, is their
implications for the calculation of the default probability and credit spreads
as the time to default, or the maturity of debt, shrinks. Under normal BlackScholes-Merton continuous time diffusion processes for asset values, the
probability that a firm’s asset value A will fall below its debt boundary B
(Figure 3-10) declines substantially as the default horizon T approaches
zero. Indeed, the implication of structural models is that the credit spread at
the very short end of the risky debt market should be zero.46
In general, however, observable short-term credit spreads are
nonzero. It could be argued that this is due to liquidity and transaction
cost effects, but there is a conflicting opinion that the structural models of
the Black-Scholes-Merton and KMV types—and especially the underlying
assumptions of these models regarding the diffusion of asset values over
time (see Figure 3-10)—underestimate the probability of default over
short horizons.47 Recent research efforts have focused on resolving this
issue by modifying the basic assumptions of the Black-Scholes-Merton
model. The work by Zhou48 attempts to address underestimation of short-
horizon risk by allowing for jumps in the asset value A of the firm. Related
work on intensity-based models by Jarrow and Turnbull49 and by Duffie and
Singleton50 presents an alternative approach to resolving the short-term
horizon problem. Intensity-based models apply fixed or variable hazard
functions to default risk. Essentially, rather than assuming a structural
model of default (as in the Black-Scholes-Merton approach), in which a
firm defaults when asset values fall below debt values, the intensity-based
model is a reduced-form model; default follows a Poisson distribution,
and default arises contingent on the arrival of some hazard.51 Duffie and
Lando52 have sought to integrate the intensity based approach into the
structural Black-Scholes-Merton approach. Assume that asset values in
the context of the structural model are noisy in that they cannot be adequately observed by outsiders. In this context, accounting information releases may partially resolve this information gap and lead to jumps in
asset values as investors revise their expectations based on partial information. Thus, imperfect information and noisiness in observed asset values may potentially be integrated into the OPM (structural) framework
and resolve the underestimation of default risk at the short-term horizon.
Work by Leland,53 by Anderson, Sunderesan, and Tychon,54 and by MellaBarral and Perraudin55 extends the classic Black-Scholes-Merton model by
allowing for debt renegotiations (i.e., renegotiations of the debt boundary
value), and thus a “dynamic” B.56 Similarly, Leland57 builds in agency
costs as a friction to the traditional Black-Scholes-Merton model, and
Acharya and Carpenter58 model callable defaultable bonds under conditions of stochastic interest rates and endogenous bankruptcy.
3.8.5 J. P. Morgan’s CreditMetrics
and Other VaR Approaches Background
Since 1993, when the Bank for International Settlement (BIS) announced
its intention to introduce a capital requirement for market risk (see Section
2.5.4), great efforts have been made in developing and testing methodologies of value at risk (VaR). In 1995, the BIS amended its market risk proposal and agreed to allow certain banks to use their own internal models,
rather than the standardized model approach, to calculate their market
risk exposures. Since 1997, in the European Community and later in the
United States, the largest banks (subject to local regulatory approval) have
been allowed to use their internal models to calculate VaR exposures and
the capital requirements for their trading books.59
The following sections review some general VaR concepts and subsequently discuss its potential extension to nontradable loans and its substitution or enhancement as a model for the 8 percent risk-based capital
ratio currently applied when calculating the capital requirement for loans
Credit Risk
in the banking book. The focus is on CreditMetrics, developed by J. P.
Morgan in conjunction with several other sponsors, including KMV. Conceptual VaR Approach
Essentially, VaR models seek to measure the maximum loss of value on a
given asset or liability over a given time period at a given confidence level
(e.g., 95 percent, 97.5 percent, 99 percent, etc.).
This book defines VaR as the predicted worst-case loss at a specific
confidence level over a certain period of time.
An example of a tradable instrument such as a corporate bond will
suffice to describe the basic concept of VaR methodology (see Figure 3-11).
Assume that the market price P of a corporate bond today is $80, and the
estimated daily standard deviation of the value σ is $10. Because the trading book is managed over a relatively short horizon (usually with a
one-day time horizon), a trader or risk manager may ask: “What is the potential loss tomorrow expressed in dollars at a 95 percent confidence
level?” Assume that the trader is concerned with the potential loss on a
bad day that occurs, on average, once in every 100 days, and that daily
asset values (and thus returns) are normally distributed around the current bond value of $80. Statistically speaking, the one bad day has a 1
percent probability of occurring tomorrow. The area under a normal distribution function carries information about probabilities. Roughly 68
percent of return observations must lie between +1 and −1 standard deviation from the mean; 95 percent of observations lie between +2 and −2
standard deviations from the mean; and 98 percent of observations lie between +2.33 and −2.33 standard deviations from the mean. With respect to
the latter, and in terms of dollars, there is a 1 percent chance that the value
of the bond will increase to a value of $80 + 2.33σ tomorrow, and a 1 percent chance that it will fall to a value of $80 − 2.33σ. Because σ is assumed
to be $10, there is a 1 percent chance that the value of the bond will fall to
$56.70 or below; alternatively, there is a 99 percent probability that the
bond holder will lose less than $80 − $56.70 = $23.30 in value; that is, $23.30
can be viewed as the VaR on the bond at the 99 percent confidence level.
Note that, by implication, there is a 1 percent chance of losing $23.30 or
more tomorrow. As, by assumption, asset returns are normally distributed, the 1 bad day in every 100 can lead to the loss being placed anywhere in the shaded region below $56.70 in Figure 3-11. In reality, losses
on nonleveraged financial instruments are truncated at −100 percent of
value, and the normal curve is at best an approximation to the log-normal.
The key input variables for the VaR calculation of a tradable instrument are its current market value P and the volatility or standard deviation of that market value σ. Given an assumed risk horizon (number of
days, weeks, etc.) and a required confidence level (e.g., 99 percent), the
VaR can be directly calculated.
F I G U R E 3-11
VaR Exposure for a Traded Instrument for a Specific Time Horizon.
P = $ 80.00
2.33σ = $ 23.30
P = $ 56.70
0 (current)
1 day
Time t
Application of this standardized methodology to nontradable loans
creates direct problems:
The current market value of a loan P is not directly observable, as
most loans are not traded.
As P is not observable, no time series is available to calculate σ,
the volatility of P.
At best, the assumption of a normal distribution for returns on some
tradable assets is a rough approximation, and the assumed approximation
becomes critical when applied to the possible distribution of values for
loans. Specifically, loans have both severely truncated upside returns and
long downside risks (see Figure 3-12). As a result, even if we can and do
measure P and σ, we still need to take into account the asymmetry of returns on making a loan. CreditMetrics
CreditMetrics was introduced in 1997 by J. P. Morgan and its cosponsors
(Bank of America, KMV, Union Bank of Switzerland, and others) as a VaR
framework to apply to the valuation and risk of nontradable assets such as
loans and privately placed bonds.60 RiskMetrics seeks to answer the question: “If tomorrow is a bad day, how much will I lose on tradable assets
Credit Risk
F I G U R E 3-12
Nonnormal Distributed Returns and Impact on VaR Calculation. (Source: J. P. Morgan, CreditMetrics Technical Document, New York: J. P. Morgan, April 2, 1997, 7,
chart 1.1. Copyright © 1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.)
such as stocks, bonds, and equities?” CreditMetrics asks: “If next year is a
bad year, how much will I lose on my loans and loan portfolio?”61
As mentioned earlier, loans are not publicly traded, thus neither P
(the loan’s market value) nor σ (the volatility of the loan value over the
specified horizon) can be observed directly. However, using the following
information, it is possible to calculate a hypothetical P and σ for any nontraded loan or bond, and, thus, a VaR figure for individual loans and the
loan portfolio.62
Available data on a borrower’s credit rating
The probability that the rating will change over the next year (the
rating transition matrix)
Recovery rates on defaulted loans (empirical data)
Credit spreads and yields in the bond or loan market (market data)
The first step is the calculation of the VaR on a loan using a simple
example; the second step is consideration of technical issues arising from
the calculation. Consider, as the example, a five-year fixed-rate loan of
$100 million at 6 percent annual interest.63 The borrower is rated BBB.
Rating Migration
Based on historical data on publicly traded bonds and loans collected by
Standard & Poor’s, Moody’s, KMV, or other bond or loan analysts, the
probability that a BBB borrower will stay at BBB over the next year is estimated at 86.93 percent.64 There is also some probability that the borrower
will be upgraded (e.g., to A) or will be downgraded (e.g., to CCC or even
to default, D). Indeed, eight transitions are possible for the borrower during the next year. Seven involve upgrades, downgrades, and no rating
change, and one involves default.
The effect of rating upgrades and downgrades is to reflect the required
credit risk spreads or premiums (based on the changed ratings) on the
loan’s remaining cash flows and, thus, on the implied market (or present)
value of the loan. If a loan is downgraded, the required credit spread premium should increase, so that the outstanding present value of the loan to
the financial organization should decrease. The contractual loan rate in the
example is assumed fixed at 6 percent. A credit rating upgrade has the opposite effect. Technically, because we are revaluing the five-year, $100 million, 6 percent loan at the end of the first year, after a credit event has
occurred during that year, then (measured in millions of dollars):65
P = 6 + ᎏᎏ + ᎏᎏ2 + ᎏᎏ3 + ᎏᎏ4
1 + r1 + s1 (1 + r2 + s2)
(1 + r3 + s3)
(1 + r4 + s4)
where ri are the risk-free rates (so called forward zero rates) on zerocoupon T-bonds expected to exist one year into the future, and the one-year
forward zero rates are calculated from the current treasury yield curve.
Further, s is the annual credit spread on zero-coupon loans of the particular rating class of one-year, two-year, three-year, and four-year maturities
(the latter are derived from observed spreads in the corporate bond market over treasuries). In the example, the first year’s coupon or interest payment of $6 million is undiscounted and can be regarded as accrued
interest earned on a bond or a loan.
Assume that during the first year, the borrower gets upgraded from
BBB to A. The present or market value of the loan to the financial organization at the end of the one-year risk horizon (in millions) is then:66
P = 6 + ᎏ + ᎏ2 + ᎏ3 + ᎏ4 = $108.66
1.0372 (1.0432)
At the end of the first year, if the loan borrower is upgraded from
BBB to A, the $100 million (book value) loan has a market value to the financial organization of $108.66 million. (This is the value the financial organization would theoretically be able to obtain at the year-1 horizon if it
sold the loan to another financial organization at the fair market price.)
Table 3-5 shows the value of the loan if other credit events occur. Note that
Credit Risk
T A B L E 3-5
Value of the Loan at the End of Year 1, Under Different Ratings
(Including First-Year Coupon)
Year-End Rating
Value, Millions
Transition Probability, %
SOURCE: J. P. Morgan, CreditMetrics Technical Document, New York: J. P. Morgan, April 2, 1997, 11. Copyright © 1997 by
J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.
the loan has a maximum market value of $109.37 million (if the borrower
is upgraded from BBB to AAA) and an estimated minimum value of
$51.13 million if the borrower defaults. The latter is the estimated recovery
value of the loan, or one minus the loss given default (LGD) if the borrower declares bankruptcy.67
The probability distribution of loan values is shown in Figure 3-13.
The value of the loan has a relatively fixed upside and a long downside
(i.e., a negative skew). The value of the loan is not symmetrically (or normally) distributed.
The maps are based on the rating transitions (nonnormal), whereas
the returns of the underlying assets (loans) are assumed to be normally
distributed. The VaR calculation in CreditMetrics has normally and nonnormally distributed components. In order to see how accurate the assumption of normal distribution is, we can now calculate two VaR
measures, based on the normal and the actual distribution of loan values,
Calculation of VaR
Table 3-6 demonstrates the calculation of the VaR, based on two approaches, for both the 5 and 1 percent worst-case scenarios around the
mean or expected (rather than original) loan value. Step 1 in determining
VaR is to calculate the expected mean of the loan’s value (or its expected
value) at year 1. This is calculated as the sum of each possible loan value
at the end of the year times its transition probability over this one-year pe-
F I G U R E 3-13
Distribution of Loan Values on Five-Year BBB Loan at the End of Year 1. (Source:
J. P. Morgan, CreditMetrics Technical Document, New York: J. P. Morgan, April 2,
1997, 11, chart 1.2. Copyright © 1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.)
riod. The mean value of the loan is $107.09 (also see Figure 3-14). However, the financial organization is interested in knowing the unexpected
losses or volatility in the loan’s value. Specifically, if next year is a bad
year, how much can the organization lose at a certain probability level? A
bad year could be defined as occurring once every 20 years (the 5 percent
confidence level) or once every 100 years (the 1 percent confidence level).
This definition is similar to market risk VaR, except that for credit risk, the
risk horizon is one year rather than one day.
Assuming that loan values are normally distributed, the variance of
loan value (in millions) around its mean is $8.94 (squared), and its standard
deviation, or volatility, is the square root of the variance, equal to $2.99.
Thus, the VaR on a 5 percent confidence level for the loan is 1.65 × $2.99 =
$4.93 million. The VaR on a 1 percent confidence level is 2.33 × $2.99 = $6.97
million. However, this likely underestimates the actual or true VaR of the
loan, because, as shown in Figure 3-14, the distribution of the loan’s value
is clearly not normal. In particular, it demonstrates a negative skew or a
long-tailed downside risk.
Applying the current distribution of loan values and probabilities in
Table 3-6 results in a 6.77 percent probability that the loan value will fall
below $102.02, implying an approximate VaR on a 5 percent confidence
level of $5.07 million ($107.09 − $102.02 = $5.07 million), and a 1.47 percent
probability that the loan value will fall below $98.10, implying an approxi-
Credit Risk
T A B L E 3-6
VaR Calculations for the BBB Loan (Benchmark Is Mean Value of Loan)
New Loan
Value Plus
Value, $
Difference of
Value from
Mean, $
$107.09 =
mean value
8.94 =
variance of
σ = standard deviation = $2.99
Assuming normal distribution:
5 percent VaR = 1.65σ = $4.93
1 percent VaR = 2.33σ = $6.97
Assuming actual distribution:*
5 percent VaR
95 percent of actual distribution = $107.09 − $102.02 = $5.07
1 percent VaR
99 percent of actual distribution = $107.09 − $98.10 = $8.99
*5% VaR approximated by 6.77% VaR (i.e., 5.3% + 1.17% + 0.12% + 0.18%) and 1% VaR approximated by 1.47% VaR
(i.e., 1.17% + 0.12% + 0.18%).
SOURCE: J. P. Morgan, CreditMetrics Technical Document, New York: J. P. Morgan, April 2, 1997, 28. Copyright © 1997 by
J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.
mate VaR on a 1 percent confidence level of $8.99 million ($107.09 − $98.10 =
$8.99). These current VaR measures could be made less approximate by applying a linear interpolation to get at the 5 and 1 percent confidence levels.
For example, because the 1.47 percentile equals $98.10 and the 0.3 percentile
equals $83.64, using linear interpolation, the 1.00 percentile equals approximately $92.29. This suggests an actual 1 percent VaR of $107.09 − $92.29 =
$14.80.68 Capital Adequacy Requirements
The critical test for a credit model is to compare these VaR figures with the
8 percent risk-based capital requirement against loans that is currently
mandated by the BIS and the Federal Reserve. For a $100 million face
F I G U R E 3-14
Actual Distribution of Loan Values on Five-Year BBB Loan at the End of Year 1.
$51.13 m
$107.09 m
= mean
Value of loan
$109.37 m
(book) value BBB loan to a private-sector borrower, the capital requirement would be $8 million. (Note the contrast to the two VaR measures developed previously.) Using the 1 percent VaR based on the normal
distribution, the capital requirement against unexpected losses on the loan
would be $6.97 million (i.e., less than the BIS requirement). Using the 1
percent VaR based on the interpolated value from the actual distribution,
the capital requirement would be $14.80 million (an amount much greater
than the BIS capital requirement).69 Implementing the CreditMetrics approach, every loan is likely to have a different VaR and thus a different implied or economic capital requirement. This contrasts with the current BIS
regulations, in which all loans of different ratings (AAA to CCC) and different maturities are subject to the same 8 percent capital requirement.
Moreover, the question of a stress-test multiplier for an internally based
capital requirement would also need to be addressed. In particular, estimated losses at the 99 percent confidence level have a distribution which
might exceed the boundaries in extreme events. In extreme events (such as
a catastrophic year), the loss will exceed the 99 percent measure calculated
by a significant margin. Under the BIS approach to support market risk,
this extreme loss (or stress-test issue) is addressed by requiring banks to
multiply their estimated VaRs by a factor ranging between 3 and 4.70
Applying such a multiplication factor in the credit risk context to
low-quality loans would raise capital requirements considerably. The
process to derive the appropriate size of such a multiplication factor, given
Credit Risk
the problems of stress testing credit risk models, remains a critical issue
for the success of credit risk models in the capital requirement context. Technical Challenges and Solution Approaches
Rating Migration
A number of questions arise in applying the bond-rating transitions assumed in Table 3-6 to calculate the transition probabilities of ratings moving to different rating categories (or to default) over the one-year horizon:
First, the way defaults and transitions occur and the transition
probabilities are calculated is mapped in CreditMetrics with an
average one-year transition period over past data (e.g., 20
years).71 Specifically, the transition probabilities are assumed to
follow a stable Markov process,72 which assumes that the
probability that a bond or loan will transition to any particular
level during this period is independent of (not correlated with)
any outcome in the past period. However, there is empirical
evidence that rating transitions are autocorrelated over time.
For example, a bond or loan that was downgraded in the
previous period has a higher probability of being downgraded
in the current period (compared to a borrower or a loan that
was not downgraded).73 This suggests that the ratings
transitions can be described better with a second or higher
Markov over time.
Second, the transition matrix stability is assumed to be stable. The
use of a single transition matrix assumes that transitions do not
differ across borrower types (a detailed segregation of industrial
firms versus banks, or Europe versus the United States) or across
time (e.g., peaks versus troughs in the business cycle). There is
considerable empirical evidence to assume that important
industry factors, such as country factors or business cycle factors,
impact rating transitions. For example, when analyzing a loan to
a German industrial company, it is required to apply a rating
transition matrix built around data for that specific country and
industry. CreditPortfolioView, analyzed later in this chapter, can
be regarded as a direct attempt to manage the issue of cyclical
impact on the bond or loan transition matrix.74
The third issue relates to the portfolio effect of bonds used in
calculating the transition matrix. Altman and Kishore found a
noticeable empirical impact of bond “aging” on the probabilities
calculated in the transition matrix.75 Indeed, a substantial impact
has been found, depending on whether the bond sample used to
calculate transitions is based on new bonds or on all bonds
outstanding in a rating class during a specific time frame.
The fourth issue relates to the methodology of applying bond
transition matrices to value loans. As collateral, covenants, and
other features make loans behave differently from bonds,
applying bond transition matrices may result in an inherent
valuation bias. This demands the internal development, by the
banks, of loan-rating transitions based on historic loan databases,
as a crucial step to improve the methodological accuracy of VaR
measures of loan risk.76
In the VaR calculation, as shown earlier, the amount recoverable on default (assumed to be $51.13 per $100 in this example), the forward zero interest rates ri , and the credit spreads si are all assumed to be nonstochastic.
Making any or all of them stochastic generally will increase any VaR
measure and thus capital requirement. In particular, loan recovery rates
have substantial variability, and the credit spread has empirically different
sizes, where the credit spread variability is expected to vary over some rating class at a given moment in time (e.g., AAA and A+ bonds or loans are
likely to have different credit spreads).77 More generally, credit spreads
and interest rates are likely to vary over time with the credit cycle and
shifts, rotation, and convexity in the term structure, rather than being deterministic.
Another topic to mention is recovery rates. If the standard deviation
of recovery rates is $25 to $45, around a mean value of $51.13 per $100 of
loans, it can be shown that the VaR (assuming the 99 percent confidence
level) will increase to 2.33 × $3.13 million = $7.38 million, or a VaR-based
capital requirement of 7.38 percent of the face value of the BBB loan.78 One
reason for assuming that interest rates are nonstochastic or deterministic
is to separate market risk from credit risk.79 But this remains highly controversial, especially to those who feel that their measurement should be
integrated rather than separated and that credit risk is positively correlated with the interest-rate cycle.80
Mark-to-Market Model versus Default Model
By allowing for the effects of credit-rating transitions (and hence, spread
changes) on loan values, as well as default, CreditMetrics is viewed as a
mark-to-market (MTM) model. Other models, such as CreditRisk+, attribute spread risk as part of market risk and concentrate on calculation of expected and unexpected loss rather than on expected and unexpected
changes in value as in CreditMetrics. This alternative approach is often
called the default model or default mode (DM). (See Section
It is useful to compare the effects of the MTM model versus the DM
model by calculating the expected and, more important, the unexpected
losses for the same example.
Credit Risk
The expected loss on the loan is:
Expected loss = p × LGD × exposure
To calculate the unexpected loss, some assumptions regarding the
default probability distributions and recoveries have to be made. The simplest assumption is that recovery rates are fixed and are independent of
the distribution of probabilities. As the borrower either defaults or does
not default, the default probability can, most simply, be assumed to be binomially distributed with a standard deviation of:
σ = 兹苶
p × (1 苶
− p)
The unexpected loss on the loan (given a fixed recovery rate and exposure amount) is:
Unexpected loss = 兹苶
p × (1 苶
− p) × LGD × exposure
The difference between the MTM and the DM approaches occurs
partly because the MTM approach allows an upside as well as a downside
transition to the loan’s value, whereas the DM approach fixes the maximum upside value of the loan to its book or face value of $100 million.
Thus, economic capital under the DM approach is more closely related to
book value accounting concepts than to the market value accounting concepts as applied in the MTM approach.
3.8.6 The McKinsey Model and Other
Macrosimulation Models Background
The current methodology underlying CreditMetrics VaR calculations assumes that transition probabilities are stable across borrower types and
across the business cycle. The assumption of stability is critical to the
CreditMetrics approach. A recent survey of the internal rating systems of
18 major bank holding companies suggested that as much as 60 percent
of their collective loan portfolios may be below the equivalent of investment grade.81 The study concludes further that the default rates on lowquality credits (including junk bonds) are highly sensitive to the state of
the business cycle. Moreover, there is empirical evidence that rating transitions in general may be correlated to the state of the economy.82 This empirical evidence suggests that the probability of downgrades and defaults
may be significantly greater in a cyclical downturn than in an upturn, assuming that transitions do not follow a normal distributed probability
180 Incorporating Cyclical Factors
There are at least two approaches to how to incorporate cyclical factors:
The past sample period is segregated into recession years and
nonrecession years (a recession matrix and a nonrecession matrix)
to yield two separate VaR calculations to calculate two separate
historic transition matrices.
The Relationship between transition probabilities and
macrofactors is modeled directly, and in a secondary step, a
model is fitted to simulate the evolution of transition probabilities
over time by shocking the model with macroevents.
McKinsey’s CreditPortfolioView is based on the second approach. The Macrosimulation Multifactor Approach
One way to build in business cycle effects and to take a forward-looking
view of VaR is to model macroeffects, both systematic and unsystematic,
on the probability of default and associated rating transitions. The
macrosimulation approach should be viewed as complementary to CreditMetrics, which overcomes some of the biases resulting from assuming
static or stationary transition probabilities period to period.83
The essential concept is represented in the transition matrix for a
given country, as shown in Figure 3-15. Note especially the cell of the matrix in the bottom right-hand corner, pCD.
F I G U R E 3-15
Historic (Unconditional) Transition Matrix.
End of period
of period
Credit Risk
Each cell in the transition matrix shows the probability that a particular counterparty, rated at a given grade at the beginning of the period,
will move to another rating by the end of the period. In Figure 3-15, pCD
shows the estimated probability that a C-rated borrower (in this example
a speculative-grade borrower) will default over the next year—that is, it
will transition from a C rating to a D rating.
In general, it can be expected that this probability moves significantly during the business cycle and is higher in recessions than in expansions. Because the probabilities in each row of the transition matrix must
sum up to 1, an increase in pCD must be compensated for by a decrease in
other probabilities—for example, those involving upgrades of initially Crated debt, where pCB and pCA represent the probabilities of the C-rated
borrower’s moving to, respectively, a B grade and an A grade during the
next year. The probability density in the transition matrix moves increasingly in a southeast direction as a recession proceeds.84
With this in mind, let pCD vary at time t along with a set of factors indexed by variable y. For convenience, the subscripts C and D will be
dropped. However, there is an implicit probability that a C-rated borrower will default over the next one-year period. In general terms:85
pt = f(yt)
where f < 0
That is, there is an inverse correlation between the state of the economy and the default probability. The macroindicator, variable y, can be
viewed as being driven by a set of i systematic macroeconomic variables
at time t (Xit) as well as by unsystematic random shocks, structural
changes to the economic system such as innovations, new industries and
technology, and the like. In general:
Yt = g(Xit, Vt)
where i = 1, . . . , n
Vt ∼ N(0, σ)
In turn, macroeconomic variables Xit, such as gross domestic product
(GDP) growth, unemployment, and so on, can themselves be considered
to be explained by their past histories (e.g., lagged GDP growth) as well as
to be sensitive to shocks themselves, εit.86 Thus:
Xit = h(Xit − 1, Xit − 2 , . . . , εit)
Different macromodel specifications can be applied in the context of
Equations (3.16) and (3.17) to improve model fit, and different models can
be used to explain transitions for different countries and industries.
Substituting Equation (3.17) into Equation (3.16), and Equation (3.16)
into Equation (3.15), the probability that a speculative grade-C loan will
transition to grade D during the next year will be determined by:
pt = f(Xit − j;Vt, εit)
Equation (3.18) models the determinants of this transition probability
as a function of lagged macrovariables, a general economic shock factor or
innovation Vt, and shock factors or innovations for each of the i macrovariables εit. Because the Xit − j are predetermined, the key variables driving pt
will be the innovations or shocks Vt and εit. Using a structured Monte Carlo
simulation approach (see Monte Carlo Simulation in Section, values for Vt and εit can be generated for periods in the future that occur with
the same probability as that observed from history.87 We can use the simulated V and ε values, along with the fitted macromodel, to simulate scenario values for pCD in periods t, t + 1, t + 2, . . . , t + n, and on into the future.
Suppose that, based on current macroconditions, the simulated
value for pCD, labeled p*, is 0.35, and the number in the historic (unconditional) transition matrix is 0.30 (where the asterisk indicates the simulated
value of the transition probability). Because the unconditional transition
value of 0.30 is less than the value estimated conditional on the macroeconomic state (0.35), we are likely to underestimate the VaR of loans and a
loan portfolio, especially at the low-quality end. Defining the ratio rt:
p*t 0.35
rt = ᎏ = ᎏᎏ = 1.16
pt 0.30
Based on the simulated macromodel, the probability of a C-rated borrower’s defaulting over the next year is 16 percent higher than the average
unconditional historical transition relationship implies. We can also calculate this ratio for subsequent periods t + 1, t + 2, and so on. For example,
suppose that, based on simulated innovations and macrofactor relationships, the simulation predicts p*t + 1 to be 0.38. The ratio relevant for the
next year, rt + 1, is then:
p*t + 1 0.38
rt + 1 = ᎏᎏ = ᎏᎏ = 1.267
pt + 1 0.30
The unconditional transition matrix will underestimate the predicted risk
of default on low-grade loans in this period.
These calculated ratios can be used to adjust the elements in the projected t, t + 1, . . . , t + n transition matrices. In McKinsey’s CreditPortfolioView, the unconditional value of pCD is adjusted by the ratio of the
conditional value of pCD to its unconditional value. Consider the transition
Credit Risk
F I G U R E 3-16
Conditional Transition Matrix Mt.
End of period
Mt =
matrix for period t; then rt × 0.30 = 0.35 (which is the same as p*t ), thus replacing 0.30 with 0.35 in the transition matrix pCD, as shown in Figure 3-16.
This also means that all the other elements in the transition matrix have to
be adjusted (e.g., pCA, pCB, and so on). A number of procedures can be used
to do this, including linear and nonlinear regressions of each element or
cell in the transition matrix on the ratio rt.88 The rows of the transition matrix must sum up to 1.89
For the next period (t + 1), the transition matrix would have to be
similarly adjusted by multiplying the unconditional value of p by rt + 1, or
0.30 × 1.267 = 0.38. This is shown in Figure 3-17.
Thus, there would be different transition matrices for each year into
the future (t, t + 1, . . . , t + n), reflecting the simulated effect of the macroeconomic shocks on transition probabilities. This type of approach, along
with CreditMetrics, could be used to calculate a cyclically sensitive VaR
for 1 year, 2 years, . . . , n years.90
Specifically, the simulated transition matrix M would replace the historically based unconditional (stable Markov) transition matrix, and,
given any current rating for the loan (say C), the distribution of loan values based on the macroadjusted transition probabilities in the C row of the
matrix Mt could be used to calculate VaR at the one-year horizon, in a fashion similar to that used by CreditMetrics in Section
F I G U R E 3-17
Conditional Transition Matrix Mt + 1.
End of period
Mt+1 =
We could also calculate VaR estimates using longer horizons. Suppose we are interested in transitions over the next two years (t and t + 1).
Multiplying the two matrices,
Mt′t + 1 = Mt ⋅ Mt + 1
produces a new matrix, Mt′t + 1. The final column of this new matrix will
give the simulated (cumulative) probabilities of default on differently
rated loans over the next two years.
The macrosimulation approach described until now considered just
one simulation of values for p*, from one set of shocks Vt and εit. This
process has to be repeated over and over again—for example, taking
10,000 random draws to generate 10,000 estimates of pt* and 10,000 possible transition matrices.
As shown in Figure 3-18, hypothetical simulated values can be plotted. The mean simulated value of p* is 0.30, but the extreme value (99th
percentile, or worst-case value) is 0.55. Calculating capital requirements
when considering unexpected declines in loan values (the latter figure for
and the transition matrix associated with this value, might be considt
ered most relevant for the capital requirement calculation.
Credit Risk
F I G U R E 3-18
Probability, %
Probability Distribution of Simulated Values.
Expected (mean)
99th percentile
(maximum) value
3.8.7 KPMG’s Loan Analysis System and Other
Risk-Neutral Valuation Approaches Background
The application of risk-neutral probabilities to value risky assets has been
in the finance literature at least as far back as Arrow (1953)91 and has been
subsequently enhanced by Harrison and Kreps (1979),92 Harrison and
Pliska (1981),93 and Kreps (1982).94 Traditionally, valuing risky assets by
discounting cash flows is done on an asset by a risk-adjusted discount
rate. To do this, the probability distribution for all cash flows and the riskreturn preferences of investors have to be known or estimated. The latter
are especially difficult to incorporate into the calculation. Suppose that all
assets are assumed to trade in a market in which all investors are willing
to accept, from any risky asset, the same expected return as that promised
by the risk-free asset. Such a theoretical market can be described as behaving in a risk-neutral fashion. In a financial market in which investors
behave in a risk-neutral manner, the prices of all assets can be determined
by simply discounting the expected future cash flows on the asset by the
risk-free rate.95
The equilibrium relationship, where the expected return on an asset
equals the risk-free rate, can be applied to back out an implied risk-neutral
probability of default, also called the equivalent martingale measure. This
forward-looking estimate of the default risk of a security can be compared
with historical estimated measures of transition probabilities. As long as an
asset is risky, the forward-looking risk-neutral probability will not equal its
historical measure (the realized value of the transition probability).96 Deriving Risk-Neutral Probabilities
The following paragraphs discuss two ways of deriving forward-looking
default probability measures based on the risk-neutral valuation approach. After that is a discussion of the relationship between the riskneutral measure of default and its historical measure. The last discussion
focuses on the potential use of the risk-neutral concept in pricing loans
and in calculating the market value of a loan and its VaR. Deriving Risk-Neutral Measures
from Spreads on Zero-Coupon Bonds
One methodology for deriving risk-neutral probabilities from spreads between risky bonds (ratings less than AAA; e.g., corporate bonds) and Treasuries has been used at Goldman Sachs and was described by Litterman
and Iben.97
Consider the two zero-coupon bond yield curves shown in Figure
3-19. The annualized discount yield on one-year zero-coupon Treasuries
is assumed to be 10 percent, and the annualized discount yield on oneyear grade-B zero-coupon corporates is 15.8 percent. The methodology
assumes that the zero-yield curves either exist or can be fitted. As noted
F I G U R E 3-19
Comparison of the Zero-Coupon Treasury Bond Curve and the Zero-Coupon
Grade-B Corporate Bond Curve.
Zero-coupon corporate bonds (B rating)
18 %
Zero-coupon Treasury bonds
15 %
11 %
10 %
Time horizon
Credit Risk
previously, in equilibrium, under risk-neutral valuation, the expected return on the risky bond must equal the risk-free return (the return on the
risk-free Treasury bond), or:
p1 × (1 + k1) = 1 + i 1
p1 = implied risk-neutral probability of repayment in year 1
1 + k 1 = expected return on risky one-year corporate bond
1 + i1 = risk-free return on one-year Treasury bond
We assume that if the risky bond defaults, the loss given default (LGD)
equals 1, and the holder of the bond receives nothing (for simplicity).
From Equation (3.22), we can derive the implied risk-neutral probability of repayment p:
1 + k1
p1 = ᎏ ᎏ = ᎏᎏ = 0.95
1 + i 1 1.158
Thus, the risk-neutral probability of default p*1 is:
p*1 = 1 − p1 = 1 − 0.95 = 0.05
We can also back out the risk-neutral probability of default in the
year 2, . . . , year n by exploiting the forward rates embedded in the zero
curves in Figure 3-19. For example, p*2, the risk-neutral probability of default in year 2 (essentially, the forward marginal probability that the Brated corporate borrower will default between year 1 and year 2), can be
derived in a two-step process. The first step is to derive the one-year expected forward rates on corporates and Treasuries from the existing zero
curves. The second step is to back out the implied risk-neutral probability of default from the forward rates. By applying this approach, the entire term structure of forward-looking risk-neutral probabilities can be
derived. Deriving the Risk-Neutral Probability
Measure from Stock Prices
Using bond prices and yield spreads, the preceding approach extracts
the risk-neutral probability of default forecast for a particular borrower
(e.g., rate B). This involves placing the borrower into a particular rating
bucket. Thus, this implies a matched yield curve for that rating class and
utilizes relationships between zero-coupon bond prices and yields for
risky versus risk-free debt. An alternative approach is to exploit the type
of option-pricing models discussed in Section 2.4.5, along with stock
prices and the volatility of stock prices. A risk-neutral probability fore-
cast for a particular borrower can also be backed out of an option-pricing
model.98 Indeed, from a Merton-type model, where equity is viewed as a
call option on the value of the firm’s assets, the probability that the value
of a firm’s assets at the time of debt maturity (e.g., T = 1) will be greater
than the face value of the firm’s debt is N1(k). The risk-neutral probability of default is then:
p*t = 1 − N1(k)
N1(k) is the area under the normal distribution relating to a variable k,
which, in turn, depends on the value of the firm’s assets, the volatility of
the firm’s assets, leverage, time to maturity, and the risk-free rate. As with
the KMV approach, neither the market value nor the volatility of the
firm’s assets is directly observable. These values have to be iterated from
observable stock prices and the volatility of stock prices. Delianedis and
Geske99 have shown that using the risk-neutral probabilities derived from
a standard Merton model100 as a first step and the risk-neutral probabilities derived from an enhanced Merton-type model101 as a second step allows for multiple classes of debt, demonstrating the ability of these
measures to predict actual rating transitions and defaults. In other words,
the risk-neutral measure has the potential to predict changes in the historical measure.102 The Relationship Between the Historical
and the Risk-Neutral Measures
Following Ginzberg et al.103 and Belkin et al.,104 the relationship between
the risk-neutral measure and the historical measure of default probability
can be best viewed in terms of a risk premium.105 That is, the spread Φ between the returns on a one-year risk-free asset (such as a corporate bond)
will reflect the risk-neutral probability of default p*1 and some loss given
default (LGD):
Φ1 = p*1 × LGD
Alternatively, we can view the spread as compensating investors for
both an expected loss ε1 and an unexpected loss u1 on the risky bond:
Φ1 = ε1 + u1
The expected loss ε1 can, in turn, be set equal to the average or historical probability of default of this type of borrower by multiplying the
historic transition probability t1 times the LGD:106
ε1 = t1 × LGD
Credit Risk
The unexpected loss component u1 can be viewed as being equal to the
unexpected default probability of default times the LGD.107
Substituting Equation (3.28) into Equation (3.27) and incorporating
Equation (3.26) results in:
p*1 × LGD = (t1 × LGD) + u1
Given some fixed LGD, the difference between p* (the risk-neutral
probability of default) and t1 (the historical probability of default) is a risk
premium that reflects the unexpected default probability. For example, if
Φ = 1 percent, LGD = 40 percent, and t1 = 1 percent, then:
Φ1 = p*1 × LGD = (t1 × LGD) + u1
Φ1 = p*1 × 0.40 = (0.01 × 0.40) + u1 = 0.01
In the next step we solve for values of both p*1 and u1. From Equations
(3.30) and (3.31), the risk-neutral probability of default p*1 = 2.5 percent,
which is higher than the historical default probability of t1 = 1 percent, and
the unexpected loss or risk premium u1 = 0.60 percent.
Ginzberg et al.108 offer an approach to how actual U.S. credit spreads
can be segregated into an expected loss and a risk premium component.
For example, an average (par) spread of 20.01 basis points on one-year
AAA corporates over one-year Treasuries can be broken down into an expected loss component t1 × LGD of 0.01 basis points and a risk premium
u1 of 20 basis points. An 1188.97 basis-point spread on one-year CCC
bonds over Treasuries can be broken down into an expected loss component of 918.97 basis points and an unexpected loss component of 270
basis points. Risk-Neutral Probabilities Applied
to Credit Risk Valuation
Risk-neutral probabilities offer substantial potential value for a credit officer in pricing decisions and in making market valuations of loans. For example, risk-neutral probabilities can be used in setting the required spread
or risk premium on a loan. Following Ginzberg et al.,109 assume a credit officer wants to find the fixed spread W on a one-year loan that will yield $1
of expected NPV from each $1 lent. The loan would be a break-even project in an NPV sense. The credit officer knows that:
r = one-year risk-free rate = 4 percent
p*1 = risk-neutral probability of default = 6.5 percent
LGD = 33.434 percent
To solve for s:
E(NPV) = (1 − p*1)(1 + r + s) + p*1(1 − LGD)
= (0.935)(1.04 + s) + 0.65(0.66566)
The value of the loan spread s that solves Equation (3.32) is 2.602 percent. However, a major problem with this approach is seen in extending
this type of analysis beyond the one-year horizon. The default or nodefault scenario, under which risk-neutral probabilities are derived, fits
the one-year loan case but not the multiyear loan case. For multiyear
loans, a richer universe of possibilities exists. These include borrower migration upgrades and downgrades, which may trigger some loan repricing clauses, which may in turn affect the value of the loan and the
borrower’s option to prepay a loan early.
Ginzberg et al.110 and KPMG’s Loan Analysis System111 have attempted to extend the valuation framework in Equation (3.32) to multiperiod loans with a variety of options. These options include loan spread
repricing as nondefault transitions in credit quality occur and building in
penalty fees for borrowers who prepay early.
Figure 3-20, from Aguis et al.,112 describes, in a simplified fashion, the
potential transitions of the credit rating of a B-rated borrower over a fouryear loan period. Similarities with bond valuation models, especially lattice or “tree” diagrams for bond valuation (binominal model), are obvious.
Given transition probabilities, the original grade-B borrower can migrate
up or down over the loan’s life to different ratings, and may even default
and migrate to D (an absorbing state). Along with these migrations, a pricing grid that reflects the bank’s current policy on spread repricing for borrowers of different quality can be built. This methodology has the potential
to generate additional information regarding whether the credit model has
a good or bad repricing grid in an expected NPV sense—basically, whether
E(NPV) ≠ 1.
When valuing a loan in this framework, valuation takes place recursively (from right to left in Figure 3-20), as it does when valuing bonds
under binomial or multinomial models. For example, if the E(NPV) of the
loan in its final year is too high (too rich), and given some prepayment fee,
the model supports prepayment of the loan to take place at the end of period 3. Working backward through the tree from right to left, the total
E(NPV) of the four-year loan can be calculated. Moreover, the credit officer can make different assumptions about spreads (the pricing grid) and
prepayment fees to determine the loan’s value. Other parameters of a
Credit Risk
F I G U R E 3-20
Multiperiod Loan Transitions Over Many Periods. [Source: Scott D. Aguais and
Anthony M. Santomero, “Incorporating New Fixed Income Approaches into Commercial Loan Valuation,” Journal of Lending and Credit Risk Management 80/6
(February 1998), 58–65, fig. 2,
Reproduced with permission of the authors.]
EDFs for multiperiod loan migrations
Grade x
Risk grade
Grade 1
Grade 1
Grade 1
AAA to
Grade 2
Grade 2
Grade 2
AA to A
Grade 3
Grade 3
Grade 3
Grade n
Grade n
Grade n
Time horizon t
loan’s structure, such as caps, and amortization schedules, can be built in,
and a VaR can be calculated.113
The risk-neutral valuation framework supports the calculation for
both default prediction and loan valuation. Compared to historic transition probabilities, the risk-neutral model gives the advantage of a
forward-looking prediction of default. The risk-neutral prediction will
generally exceed the history-based transition prediction over some horizon because, conceptually, it contains a risk premium reflecting the unexpected probability of default. Moreover, the risk-neutral framework
considers only two credit states: default and nondefault; it does not recognize several rating buckets.
KPMG suggested a valuation approach that is potentially consistent
with the risk-neutral model under no arbitrage.114 Over its life, a loan can
migrate to states other than default/nondefault. The valuation model is
similar in spirit to a multinomial tree model for bond valuation, with the
difference that transition probabilities replace interest-rate movement
probabilities. This model has some flexibility, as credit spreads can vary,
fees can be charged on prepayments, and other special provisions can be
built into the valuation process. A question arises as to the link between
the model and the existence of an underlying portfolio of replicating assets. In particular, the exact details of the construction of a replicating noarbitrage portfolio for a multiperiod nontradable loan are still open.
3.8.8 The CSFB CreditRisk+ Model Background
Only quite recently have ideas and concepts from the insurance industry
found their way into the new approaches for credit risk measurement and
management. The following sections discuss two applications of insurance ideas, one from life insurance and one from property insurance. Altman115 and others have developed mortality tables for loans and bonds
using ideas (and models) similar to those that insurance actuaries use
when they set premiums for life insurance policies. Credit Suisse Financial
Products, a former subsidiary of Credit Suisse First Boston (CSFB), developed a model similar to the one used by household insurance vendors for
assessing the risk of policy losses in setting premiums. Migration of Mortality Approach
for Credit Risk Measurement
The concept is quite simple: based on a portfolio of loans or bonds and
their historic default experience, develop a table that can be applied in a
predictive sense for one-year or marginal mortality rates (MMRs) and for
multiyear or cumulative mortality rates (CMRs). Combining such calculations with LGDs allows us to create estimates of expected losses.116
To calculate the MMRs of a B-rated bond or loan defaulting in each
year of its life, the analyst will pick a sample of years—say, 1971 through
1998—and, for each individual year, will analyze:
MMR1 =
Total value of grade-B bonds defaulting in year 1 of issue
Total value of a B-rated bond outstanding in year 1 of issue
MMR2 =
Total value of B-rated bond defaulting in year 2 of issue
Total value of a B-rated bond outstanding in year 2 of
issue (adjusted for defaults, calls, sinking fund
redemptions, and maturities in the prior year)
And so on for MMR3, . . . , MMRn.
When the MMR for a specific individual year has been calculated,
the credit officer calculates a weighted average of all MMRs, which becomes the figure entered into the mortality table. The weights used should
Credit Risk
reflect the relative issue sizes in different years, thus biasing the results
toward the years with larger issues. The average MMR in year 1 for a particular rating bucket (M
苶) would be calculated as:
苶1 = 冱 MMR1i ⋅ wi
i = 1971
冱w =1
To calculate a CMR—the probability that a loan or bond will default
over a period longer than a year (e.g., 2 years)—it is first necessary to specify the relationship between MMRs and survival rates (SRs):
MMRi = 1 − SRi
SRi = 1 − MMRi
CMRN = 1 − ⌸ SRi
where ∏ is the geometric sum or product [SR1 × SR2 × . . . SRN] and N denotes the number of years over which the cumulative mortality rate is
calculated. Mortality Rates and Tables
Table 3-7 shows MMRs and CMRs for syndicated loans and bonds over a
five-year horizon, as computed by Altman and Suggitt.117 Looking at the
table in more detail, we can see that for the higher-grade buckets the mortality rates are quite comparable, but this is not the case for the lowestquality-rating buckets. For example, low-quality loans have substantially
higher MMRs in the first three years of life than do similarly rated bonds.
The critical question is whether high-yield loans and bonds have substantially different default profiles, or is this a statistical result due to a
relatively small sample size? In particular, although not described, each
of the MMR estimates has an implied standard error and confidence interval. It can be shown that with an increasing number of loans or bonds
in the observation sample (i.e., as n gets bigger), the standard error on a
mortality rate will fall (i.e., the degree of confidence level applied to calculate the MMR estimate of expected out-of-sample losses increases). As
a loan or bond either dies or survives in any period, the standard error T
of an MMR is:118
SOURCE: E. I. Altman and H. J. Suggitt, “Default Rates in the Syndicated Loan Market: A Mortality Analysis,” Working Paper S-97-39, New York University Salomon Center, New York, December 1997.
Reproduced with permission of NYU Salomon Center.
Years after Issue
Comparison of Syndicated Bank Loan Versus Corporate Bond Mortality Rates, Based on Original Issuance Principal Amounts (1991–1996)
T A B L E 3-7
Credit Risk
MMRi ⋅ (1 − MMRi)
σ = ᎏᎏᎏ
MMRi ⋅ (1 − MMRi)
N = ᎏᎏᎏ
and rearranging:
As can be derived from Equations (3.37) and (3.38), there is an inverse relationship between sample size N and the standard error σ of a
mortality rate estimate.
Assume that MMR1 = 0.01 is a mortality rate estimate, and extreme
actuarial standards of confidence in the stability of the estimate for pricing
and prediction out of sample have to be applied. Extreme actuarial standards might require σ to be one-tenth the size of the mortality rate estimate (or σ = 0.001). Plugging these values into Equation (3.38) results in:
(0.01) ⋅ (0.99)
N = ᎏᎏ
= 9900
This results in 10,000 loan observations per rating bucket required to
obtain this type of confidence in the estimate. With, say, 10 rating classes, a
portfolio of some 100,000 loans would have to be analyzed and calculated.
Very few banks have the resources to build information systems of this type.
To get to the requisite large size, a nationwide effort among the banks themselves may be required. The end result of such a cooperative effort might be
a national loan mortality table per country that could be used for the calculation of the banks’ loan loss reserves, based on expected losses, similar to
the national life mortality tables applied in pricing life insurance.119
3.8.9 CSFB’s CreditRisk+ Approach
This section analyzes two insurance-based approaches to credit risk analysis.
Mortality analysis offers an actuarial approach to predicting default rates,
which is considered an alternative to some of the traditional accountingbased models for measuring expected losses and loan loss reserves. The
added value of mortality rates very much depends on the size of the sample
of loans or bonds from which they are calculated. CreditRisk+, an alternative
to CreditMetrics, calculates capital requirements based on actuarial approaches found in property insurance concepts. The major advantage is the
rather minimal data input required (e.g., no data on credit spreads are required). Its major limitation is that it is not a full VaR model because it focuses on loss rates rather than loan value changes. It is a default-mode (DM)
model rather than a mark-to-market (MTM) model.
The approach developed by CSFB stands in direct contrast to CreditMetrics in its objectives and its theoretical framework:
CreditMetrics seeks to estimate the full VaR of a loan or loan
portfolio by viewing rating upgrades and downgrades and the
associated effects of spread changes in the discount rate as part of
the credit’s VaR exposure. In contrast, CreditRisk+ considers
spread risk as part of market risk rather than credit risk. As a
result, in any period, only two states of the credit world are
considered, default and nondefault. The focus is on measuring
expected and unexpected losses rather than expected value and
unexpected changes in value (or VaR) as under CreditMetrics. As
mentioned, CreditMetrics is an MTM model, whereas CreditRisk+
is a DM-based model.
The second major conceptual difference is that in CreditMetrics,
the default probability in any year is modeled based on a discrete
assumption (as are the upgrade/downgrade probabilities). In
CreditRisk+, default is modeled as a continuous variable with a
probability distribution. An analogy from home insurance is
relevant. When a whole portfolio of home loans is insured, there is
a small probability that all houses will burn down simultaneously.
In general, the probability that each house will burn down can be
considered as an independent event. Similarly, many types of
loans, such as mortgages and small business loans, can be
analyzed in a similar way, with respect to their default risk. In the
CreditRisk+ model, each individual loan is assumed to have a
small default probability, and each loan’s default probability is
independent of the default on other loans.120 This assumption of
independent occurrence makes the default probability distribution
of a loan portfolio resemble a Poisson distribution.
Figure 3-21 presents the difference in assumptions regarding default
probability distribution in CreditRisk+ and CreditMetrics.
The two degrees of uncertainty, the default frequency and the loss
severity, produce a distribution of losses for each exposure band. Summing (or, more exactly, aggregating) these losses across exposure bands
produces a distribution of losses for the loan portfolio (Figure 3-22). Although not labeled by CSFB as such, we shall call the model in Figure 3-23
Model 1. The computed loss function, assuming a Poisson distribution for
individual default rates and the bucketing of losses, is displayed in Figure
3-23. The loss function is quite symmetric and is close to the normal distribution, which it increasingly approximates as the number of loans in
the portfolio increases. However, as discussed by CSFB, default and loss
rates tend to have fatter tails than is implied by Figure 3-23.121 Specifically,
the Poisson distribution implies that the mean default rate of a portfolio of
loans should equal its variance, that is:
Credit Risk
F I G U R E 3-21
Comparison of the CreditRisk+ and CreditMetrics Models.
Credit Risk Plus
Possible paths of default rate
BBB loan
Time horizon
Possible paths of default rate
BBB loan
Time horizon
σ2 = mean
σ = 兹mean
Using figures on default rates from Carty and Lieberman,122 CSFB shows
that, in general, Equation (3.41) does not hold, especially for lower-quality
credit. For B-rated bonds, Carty and Lieberman found that the mean default rate was 7.27 percent, its square root was 2.69 percent, and its σ was
F I G U R E 3-22
Influencing Factors on Distribution of Losses.
Frequency of defaults
Severity of loss
Distribution of default losses
Default loss
5.1 percent, or almost twice as large as the square root of the mean (see
Figure 3-23). This answers the question of what extra degree of uncertainty might explain the higher variance (fatter tails) in observed loss distributions. The additional uncertainty modeled by CSFB is that the mean
default rate itself can vary over time or over the business cycle. For example, in economic expansions, the mean default rate will be low; in eco-
F I G U R E 3-23
Distribution of Credit Losses with Default Rate Uncertainty
and Severity Uncertainty.
Actual loss distribution
Model 1
Credit Risk
nomic contractions, it may rise substantially. In their extended model
(henceforth called Model 2), there are three types of uncertainty:
The uncertainty of the default rate around any given mean
default rate
The uncertainty about the loss severity
The uncertainty about the mean default rate itself, modeled as a
gamma distribution by CSFP123
Appropriately implemented, a loss distribution can be calculated
along with expected losses and unexpected losses that exhibit observable fatter tails. The latter can then be used to calculate the capital requirement, as shown in Figure 3-24. Note that this economic capital
measure is comparable with the VaR measured under CreditMetrics, because CreditMetrics allows for rating upgrades and downgrades that affect a loan’s value. By contrast, there are no nondefault migrations in the
CSFB model. Thus, the CSFB capital calculation is closer to a loss-ofearnings or book-value capital measure than a full market value of economic capital measure. Nevertheless, its great advantage lies in its
parsimonious requirement of data. The key data inputs are mean loss
rates and loss severities, for various loss buckets in the loan portfolio,
both of which are potentially amenable to collection, either internally or
externally. A simple discrete example of the CSFB Model 1 will illustrate
the minimal data input that is required.
F I G U R E 3-24
Capital Requirement Based on the CSFB CreditRisk+ Model.
Unexpected loss at 99th percentile level
Expected loss
Economic capital
Uncovered losses
3.8.10 Summary and Comparison
of New Internal Model Approaches Background
The previous sections describe key features of some of the more prominent
new quantitative models of credit risk measurement that are publicly available. At first glance, these approaches appear to be very different and likely
to generate substantially different loan loss exposures and VaR measures.
The following sections summarize and compare four of these new models
and highlight key differences and similarities among them. Model Comparison
Six key dimensions are used to compare the different approaches among
the four models: (1) CreditMetrics, (2) CreditPortfolioView, (3) CreditRisk+, and (4) KMV. Analytically and empirically, these models are not as
different as they may first appear. Indeed, similar arguments have been
made by Gordy,124 Koyluoglu and Hickman,125 and Crouhy and Mark,126
using different model anatomies. Table 3-8 displays the six key dimensions for comparing the models.
T A B L E 3-8
Comparison of Different Approaches
(J. P. Morgan)
Definition of
Risk drivers
Asset values
default rates
Asset values
Volatility of
credit events
Correlations of
credit events
normal asset
Factor loadings
correlation of
residual risk
assumption or
correlation with
expected default
normal asset
Constant with
Constant or
Simulation or
analytic (oneperiod VaR)
Credit Risk
201 Definition of Risk in the Different Models
As described in the previous sections, we distinguish between models that
calculate VaR based on the change in the market value of loans using
mark-to-market (MTM) models, and models that focus on predicting default losses using default-mode (DM) models.127 The MTM models allow
for credit upgrades and downgrades, and therefore spread changes, as
well as defaults in calculating loan value losses and gains. Contrarily, the
DM models consider only two states of the credit world: default and nondefault. The key difference between the MTM and DM approaches is the
inclusion of spread risk in MTM models. Not surprisingly, if models incorporate different input, they are likely to produce different results.
CreditMetrics is an MTM model, whereas CreditRisk+ and KMV are DM
models. CreditPortfolioView can be implemented as an MTM or a DM
model. Risk Drivers
CreditMetrics and KMV have their analytic foundations in a Merton-type
model; a firm’s asset values and the volatility of asset values are the key
drivers and input variables of default risk. In CreditPortfolioView, the risk
drivers are macrofactors (such as inflation, credit spread, etc.); in CreditRisk+, the risk drivers are the mean level of default risk and its volatility. If
expressed in terms of multifactor models, all four models can be viewed as
having similar roots.128 Specifically, the variability of a firm’s asset returns
in CreditMetrics (as well as in KMV) is modeled as being directly linked to
the variability in a firm’s stock returns. In calculating correlations among
firms’ asset returns, the stocks of individual firms are determined by a set
of systematic risk factors (industry factors, country factors, etc.) and unsystematic risk factors. The systematic risk factors, along with correlations
among systematic risk factors (and their weighted sensitivity, similar to
the multifactor/arbitrage pricing theory of model portfolio theory), determine the asset returns of individual firms and the default correlations
among firms.
The risk drivers in CreditPortfolioView have methodological foundations similar to those of CreditMetrics and KMV. In particular, a set of
local systematic market macrofactors and unsystematic macroshocks
drives default risk and the correlations of default risks among borrowers
in the same local market. The key risk driver in CreditRisk+ is the variable
mean default rate in the economy. This mean default rate can be linked systematically to the state of the macroeconomy—when the macroeconomy
deteriorates, the mean default rate is likely to rise, as are default losses.
Improvement in economic conditions has the opposite effect.
Risk drivers and correlations in all four models can be correlated to
a certain extent to macrofactors describing the evolution of economywide
CHAPTER 3 Volatility of Credit Events
A key difference in the methodology among the models is in the modeling
of the one-year default probability or the probability of default distribution function. In CreditMetrics, the default probability (as well as upgrades and downgrades) is modeled as a fixed or discrete value based on
historic data. In KMV, expected default frequencies (EDFs) are linked to
the variability of the firm’s stock returns, and will vary as new information is impounded in stock prices. Variations in stock prices and the
volatility of stock prices determine the KMV’s EDF scores. In CreditPortfolioView, the default probability is a logistic function of a set of macrofactors and normally distributed shocks. As the macroeconomy evolves,
the default probability and the cells, or probabilities, in the rest of the transition matrix will evolve as well. In CreditRisk+, the default probability of
each loan is assumed to be variable, following a Poisson distribution
around some mean default rate. The mean default rate is modeled as a
variable with a gamma distribution. This produces a distribution of losses
that may have fatter tails than those produced by either CreditMetrics or
CreditPortfolioView. Correlation of Credit Events
The similarity of the determinants of credit risk correlations has been discussed in the context of risk drivers. Specifically, the correlation structure
in all four models can be attributed to systematic sensitivities of loans to
key factors. The correlations among borrowers are discussed in Section
3.9.6, where the application of the new models and modern portfolio theory to support credit portfolio decisions is discussed. Recovery Rates
The loss distribution and VaR calculations depend not only on the default
probability but also on the loss severity or loss given default (LGD). Empirical evidence suggests that default severities and recovery rates are
quite volatile over time. More precisely, building in a volatile recovery rate
is likely to increase the VaR or unexpected loss rate.
CreditMetrics, in the context of its VaR calculations, allows for recoveries to be variable. In the current model version, which recognizes a
skew in the tail of the loan value loss distribution function, recovery rates
are assumed to follow a beta distribution, and the VaR of loans is calculated via a Monte Carlo simulation. In KMV’s simplest model, recovery
rates are considered constant over time. In more recent extended versions
of the model, recovery rates are allowed to follow a beta distribution as
well. In CreditPortfolioView, recovery rates are also estimated via a Monte
Carlo simulation approach. By contrast, under CreditRisk+, loss severities
are clustered and allocated into subportfolios, and the loss severity in any
subportfolio is considered constant over time.
Credit Risk
203 Numerical Approach
The estimation approach of VaRs, or unexpected losses, differs across
models. A VaR, at both the individual loan level and the loan portfolio
level, can be calculated analytically under CreditMetrics. This approach
becomes increasingly intractable as the number of loans in the portfolio
increases. As a result, for large loan portfolios, Monte Carlo simulation
techniques are applied to generate an approximate aggregate distribution
of portfolio loan values, and thus a VaR. Similarly, CreditPortfolioView
uses repeated Monte Carlo simulations to generate macroshocks and the
distribution of losses (or loan values) of a loan portfolio. CreditRisk+,
based on its convenient distributional assumptions (the Poisson distribution for individual loans and the gamma distribution for the mean default
rate, along with the fixed recovery assumption for loan losses in each subportfolio of loans), allows an analytic or closed-form solution to be generated for the probability density function of losses. KMV allows an analytic
solution to the loss function.
The development of internal models for credit risk measurement
and capital requirements is at an early stage. In some sense, its present
level of development can be compared to that of market risk in 1994, when
RiskMetrics first appeared and was followed by alternative methodologies such as historic simulation and Monte Carlo simulation. The credit
risk models publicly available to date have exhibited quite different approaches across a number of important dimensions. Harmonizing these
models across just a few key dimensions, however, can result in quite
comparable unexpected loss calculations. This suggests that over time,
with theoretical and model development, a consensus model or approach
may eventually emerge. To some extent, this has already happened in the
market risk modeling area, supported by regulatory incentives.
3.8.11 Comparison of Major Credit Risk Models
A variety of credit models exists, which are mainly portfolio approaches.
The different conceptual approaches of the most current applications are
summarized in the following list:
Conceptual model. Expected default frequency based on market
value of assets. Borrower defaults when available resources have
been depleted below a critical level. EDFs are linked to the
variability of the firm’s stock returns, which will vary as new
information is impounded in stock prices. Variations in stock prices
and the volatility of stock prices determine the KMV stock scores.
Modeling of concentration. A multifactor stock return model is
applied, from which correlations are calculated. The model
reflects the correlation among the systemic risk factors affecting
each firm’s asset correlation, their individual default
probabilities, and their appropriate weights. The approach to
estimate correlations is similar to that used in CreditMetrics.
However, KMV typically finds that correlations lie in the range of
0.002 to 0.15, which is relatively low.
Conceptual model. Simulation-based portfolio approach, in which
changes in debt values are modeled based on changes in rating,
and the market value of each position is a derived function of its
rating. Simulations of credit migrations are time consuming.
Modeling of concentration. Concentration risk is modeled by
sector allocation, and borrower correlation is derived from sector
correlations. Asset returns are simulated and mapped to
simulated credit migrations. Recovery rates are random variables.
Conceptual model. Insurance or actuarial type for modeling lowprobability, high-impact events. Default probability of each loan
is assumed to be a random, conditionally independent variable,
following a Poisson distribution around some mean default rate.
The mean default rate is modeled as a variable with a gamma
distribution. The default probability on each sector is different.
Modeling of concentration. Each position is allocated to sectors
that represent countries and industries. Sectors are conditionally
assumed to be independent, and one individual sector can be
used for modeling the specific risk of positions.
Conceptual model. A conditioned transition matrix is calculated,
simulating the evolution of transition probabilities over time by
generating macroshocks to the model. The simulated transition
matrix replaces the historically based unconditional (stable
Markov) transition matrix. Given any current rating for the loan,
the distribution of loan values, based on the macroadjusted
transition probabilities in the row for a specific rating of the
matrix, could be used to calculate VaR at the one-year horizon, in
a fashion similar to that used in CreditMetrics. A cyclically
sensitive VaR for 1, 2, . . . , n years can be calculated.
Modeling of concentration. Directly models the relationship between
transition probabilities and macrofactors; in a secondary step, a
model is fitted to simulate the evolution of transition probabilities
over time by shocking the model with macroevents. Each position is
allocated to sectors that represent countries and industries. Sectors
are not conditionally assumed to be independent.
Credit Risk
Depending on the conceptual approach of the model, the input parameters are different, as is the way some of the key elements of credit risk
are handled. Correlations that are inferred from equity indexes (such as
the CreditMetrics model) require a three-step process for the computation
of the credit correlation coefficient (Figure 3-25):
CreditMetrics provides the correlation coefficients describing the
comovements of various industry–country equity indexes.
The user has to define (input) how much of the variance in an
individual borrower’s credit indicator is derived from the various
country–industry indexes.
The model then computes the borrower’s credit correlation
Volatility values are critical information for the portfolio approach,
as they are the basis for the correlation calculation, a key component of the
portfolio approach. To measure portfolio VaR, one starts with the loanF I G U R E 3-25
Three-Step Process for Calculation of Credit Correlation Coefficients.
Transition rates
Forward values
value 100.0
Volatility depends on position pricing and
instrument structure as well as transition
specific volatility, which reflects price (historical and future) and the structure of the loan. The volatility depends on the issue of price and structure
as well as the transitions. The forward valuation depends on:
• Loan price and loan structure
• Collateral
• Spread and fees
• Amortization
• Tenor
• Options (e.g., prepayment, repricing or grid, term-out, and market
The portfolio distribution can be produced by simulation, using random draws of the loans’ xi values. In a second step, the end-of-period ratings are derived. In a third step, the loans are priced, based on the ratings
and other input parameters. In a fourth step, the loans are summed up to
get the portfolio value by using the values and the correlation from the
random draws. This procedure is repeated many times to derive a stable
distribution of the portfolio with the loans’ xi values (see Figure 3-26).
Instead of estimating the loans’ xi values, the distribution of common
and specific factors can be estimated by using random draws of the factors. In a first step, random draws of the factors are taken. In a second step,
the random draws of the factors are used to calculate the xi values. In a
third step, the loans are priced, based on the ratings and other input parameters. In a fourth step, the loans are summed up to get the portfolio
value by using the values and the correlation from the random draws.
This procedure is repeated many times to derive a stable distribution of
the portfolio with the loans’ xi values (see Figure 3-27).
F I G U R E 3-26
Computation of Portfolio Distribution Through Simulation Process.
2. Derive end-of-period ratings
1. Draw x i
5. Repeat
3. Price loan based on rating
4. Sum to get
portfolio value
Loan x 1
Loan x 2
Credit Risk
F I G U R E 3-27
Distribution of Common and Specific Factors Through Random Drawing.
2. Insert to form x i s
1. Draw x i
x1 = 1 - ρ ⋅ y1 + ρ ⋅ Z
6. Repeat
F (Y )
x 2 = 1- ρ ⋅ y 2 + ρ ⋅ Z
3. Derive end-of-period ratings
F (Z)
4. Price loan based on rating
Loan x 1
Loan x 2
5. Sum to get portfolio
3.9.1 Background
Default risk and credit risk exposure are commonly viewed on a singleborrower basis. Much of the banking theory literature views the personnel
at banks and similar institutions as credit specialists who, over time,
through monitoring and the development of long-term relationships with
customers, gain a comparative advantage in lending to a specific borrower or group of borrowers. (The current BIS risk-based capital ratio is
linearly additive across individual loans.) This advantage, developed by
granting (and holding to maturity) loans to a select subset of long-term
borrowers, can be viewed as inefficient from a risk–return perspective. Instead, loans publicly traded, or “swappable” with other financial organizations, could be considered as being similar to commodity-type assets
such as equities, which are freely traded at low transaction costs and with
high liquidity in public securities markets. By separating the credit-granting decision from the credit portfolio decision, a financial organization
may be able to generate a better risk–return trade-off, and offset what
KMV and others have called the paradox of credit.
Figure 3-28 illustrates the paradox of credit by applying the efficient
frontier approach to loans. Portfolio A is a relatively concentrated loan
F I G U R E 3-28
Return rf
The Paradox of Credit.
Return sp
portfolio for a traditional bank that makes and monitors loans, and holds
those loans to maturity. Portfolios B and C are on the efficient frontier of
loan portfolios. They achieve either the maximum return for any level of
risk B or the minimum risk for a given return C. To move from A to either
B or C, the bank must actively manage its loan portfolio in a manner similar to the tenets of modern portfolio theory (MPT), where the key focus
for improving the risk–return trade-off is on (1) the default correlations
(diversification) among the assets held in the portfolio and (2) a willingness, as market conditions vary, to flexibly adjust the loan allocation rather
than to make and hold loans to maturity, as is the traditional practice in
Modern portfolio theory provides a useful framework for considering risk–return trade-offs in loan portfolio management. The MPT framework provides the analytical basis for the intuitive observation that the
lower the correlation among loans in a portfolio, the greater the potential
for a manager to reduce a bank’s risk exposure through diversification.
Assuming that a VaR-based capital requirement reflects the concentration
risk and default correlations of the loan portfolio, such a diversified portfolio may have lower credit risk than a similar portfolio with loan expo-
Credit Risk
sures that are considered independently additive (as is the case with the
current BIS 8 percent capital ratio).
There are a number of problems in directly applying MPT to loans
and loan portfolios (and many bonds), including the following:
The nonnormality of loan returns
The unobservability of market-based loan returns (and, thus,
correlations) as a result of the fact that most loans are nontraded
These issues and other related problems are discussed in Section,
which analyzes approaches suggested by KMV, CreditMetrics, and other
models. Specific attention is given to how these new approaches calculate
returns, risk, and correlations of loans and loan portfolios.
3.9.2 Application to Nontraded Bonds and Credits
Modern portfolio theory has been around for almost 50 years and is now
a common portfolio management tool, used by most money managers. It
has also been applied with some success to publicly traded junk bonds
when their returns have tended to be more equitylike (price driven) than
bondlike (yield driven) and when historical returns have been available.129
With respect to most loans and bonds, however, there are problems with
nonnormal returns, unobservable returns, and unobservable correlations.
The following sections discuss various approaches to applying MPT
techniques to loan portfolios. Most of the new credit models are not fullfledged MPT models (returns are often not modeled), but their importance is in the link they show between both default correlations and
portfolio diversification and loan portfolio risk.
The consensus of the literature and the industry appears to be that
default correlations are relatively low on average, and gains through loan
portfolio diversification are potentially high. The current 8 percent BIS
risk-based capital ratio ignores correlations among loans in setting capital
requirements, and it may be an inadequate reflection of capital requirements. In particular, MPT-based models are more precise in suggesting
that loan portfolios in which individual loan default risks are highly correlated should have higher capital requirements than loan portfolios of
similar size in which default risk correlations are relatively low. In contrast, the current BIS regulations specify that the same capital requirement
is to be imposed for equally sized portfolios of private-sector loans, independent of their country, industry, or borrower composition.
3.9.3 Nonnormal Returns
Loans and bonds tend to have relatively fixed upside returns and longtailed downside risks. Thus, returns on these assets tend to show a strong
negative skew and, in some cases, kurtosis (fat-tailedness) as well. MPT is
built around a model in which only two moments—the mean and the variance—are required to describe the distribution of returns. To the extent that
the third (skew) and fourth (kurtosis) moments of returns substantially describe the distribution of asset returns, the straightforward application of
MPT models based on the simple two-moment approach becomes difficult
to justify. It can be argued that as the number of loans in a portfolio gets
bigger, the distribution of returns tends to become more normal.
3.9.4 Unobservable Returns
An additional issue relates to the fact that most loans and corporate
bonds are nontraded or are traded as OTC products at irregular intervals
with infrequent historical price or volume data. The estimation of mean
returns µ
苶 and the variance of returns σi using historic time series thus becomes challenging.
3.9.5 Unobservable Correlations
Similarly, if price and return data are unavailable, or the estimates are unreliable given the previously mentioned issues, calculating the covariance
σij or correlation ρij among asset returns also becomes difficult. The correlations are a key building block in MPT-type analysis.130
3.9.6 Modeling Risk–Return Trade-Off
of Loans and Loan Portfolios Background
The following discussion focuses on a number of ways to apply MPT-type
techniques to a loan portfolio. It distinguishes between models that seek
to calculate the full risk–return trade-off for a portfolio of loans (such as
KMV’s Portfolio Manager) and models that concentrate mostly on the risk
dimension (such as CreditMetrics) and the VaR of the loan portfolio. KMV’s Portfolio Manager
KMV’s Portfolio Manager can be considered a full-fledged modern portfolio theory optimization approach, because all three key variables—returns, risks, and correlations—are calculated. However, it can also be used
to analyze risk effects alone, as discussed later. Next is a discussion of how
the three key variables that enter into any MPT model can be calculated.
Loan Returns
In the absence of return histories on traded loans, the expected return on
the ith loan Rit over any given time horizon can be expressed as:
Credit Risk
Rit = [spreadi + feesj] − [expected lossi]
Rit = [spreadi + feesj] − [EDFi ⋅ LGDi]
The first component of returns is the spread of the loan rate over a
benchmark rate (such as LIBOR), plus any fees directly allocated to the
loan and expected over a given period (e.g., a year). Expected losses on the
loan are subsequently deducted because they can be viewed as part of the
normal cost of doing banking business. In the context of a KMV-type
model, where the expected default frequency (EDF) is estimated from
stock returns (the CreditMonitor model), then, for any given borrower, expected losses will equal EDFj × LGDj, where LGDi is the loss given default
for the ith borrower (usually estimated from the bank’s internal database).
Loan Risks
In the absence of historical return data on loans, a loan’s risk σLGD can be
approximated by the unexpected loss rate on the loan UL i — essentially,
the variability of the loss rate around its expected value EDFi × LGD.
There are several approaches in which the unexpected loss can be calculated, depending on the assumptions made about the number of creditrating transitions, the variability of LGD, and the correlation of LGDs
with EDFs. For example, in the simplest case, we can assume a DM model
in which the borrower either defaults or doesn’t default, so that defaults
are binomially distributed and LGD is fixed and constant across all borrowers. Then:
σi = ULi = 兹苶
⋅ (1 − 苶
where 兹苶
(EDFi) ⋅苶
(1 − 苶
EDFi) reflects the variability of a default-rate frequency that is binominally distributed. A slightly more sophisticated DM
version would allow LGD to be variable, but factors affecting EDFs are assumed to be different from those affecting LGDs, and LGDs are assumed
to be independent across borrowers. In this case:
σi = 兹苶
⋅ (1 − 苶
EDFi) 苶
⋅ LGD2苶
Fi ⋅ LG苶
i + ED苶
where σi is the standard deviation of borrower i’s LGD.131 If we want to develop σi measures, allowing for a full MTM model with credit upgrades
and downgrades as well as default, then σi might be calculated similarly
to CreditMetrics, as discussed later. Indeed, in recent versions of its
model, KMV produces a rating transition matrix based on EDFs and allows a full MTM calculation of σi to be made.132
Loan Correlations
One important assumption in a KMV-type approach is that default correlations are likely to be low. To see why, consider the context of the twostate DM version of a KMV-type model. A default correlation would
reflect the joint probability of two firms X and Y—say, Ericsson and
Nokia—having their asset values fall simultaneously below their debt values over the same horizon (e.g., one year). In the context of Figure 3-29, the
Ericsson asset value would have to fall below its debt value BY, and the
Nokia asset value would have to fall below its debt value BX. The joint area
of default is shaded, and the joint probability distribution of asset values
is represented by the isocircles. The isocircles are similar to those used in
geography charts to describe hills. The inner circle is the top of the hill representing high probability, and the outer circles are the bottom of the hill
(low probability). The joint probability that asset values will fall in the
shaded region is comparably low and will depend, in part, on the asset
F I G U R E 3-29
Joint Default Probabilities. [Source: Harry M. Markowitz, Portfolio Selection (2), 2d
ed., Oxford, United Kingdom: Basil Blackwell, 1992, figure 4, and KMV, CreditMonitor Overview, San Francisco: KMV Corporation, 1993; Portfolio Management
of Default Risk, San Francisco: KMV Corporation, November 15, 1993, rev. May 31,
2001, 10. Reproduced with permission of Blackwell Publishing and KMV LLC.]
Future value of Y Corp.
Future value of
business joint
Both in
Future value of X Corp.
Credit Risk
correlations between the two borrowers. In the context of the simple binomial model, for Nokia N and Ericsson E, respectively:
ρNE = ᎏᎏ
σN ⋅ σE
ρNE = ᎏᎏᎏᎏᎏ
)(1 − E苶
DFN) ⋅ 兹苶
)(1 − EDF
The numerator of Equation (3.47), σNE, is the covariance between the
asset values of the two firms, N and E. It reflects the difference between
when the two asset values are jointly distributed (JDFNE) and when they
are independent (EDFN ⋅ EDFE). The denominator, σN ⋅ σE, reflects the standard deviation of default rates under the binomial distribution for each
firm. Rather than seeking to directly estimate correlations using Equation
(3.47), KMV uses a multifactor stock-return model from which correlations are calculated. The model reflects the correlation among the systematic risk factors affecting each firm and their appropriate weights. KMV’s
approach to estimate correlations is discussed under CreditMetrics. However, KMV typically finds that correlations lie in the range of 0.002 to 0.15,
and are thus relatively low. After the estimation, the three inputs (returns,
risks, and correlations) can be used in a number of ways. One potential
use would be to calculate a risk–return efficient frontier for the loan portfolio, as discussed previously.
A second application is to measure the risk contribution of expanding lending to any given borrower. As discussed earlier, the risk (in a MPT
portfolio sense) of any individual loan will depend on the risk of the individual loan on a stand-alone basis and its correlation with the risks of
other loans. For example, a loan might be thought to be risky when
viewed individually, but because its returns are negatively correlated with
other loans, it may be quite valuable in a portfolio context by contributing
to diversification and thus lowering portfolio risk.
The effects of granting additional loans to a particular borrower also
depend crucially on assumptions made about the balance-sheet constraint
of the financial organization. For example, if investable or loanable funds
are viewed as fixed, then expanding the proportion of assets lent to any
borrower i (i.e., increasing X) means reducing the proportion invested in
all other loans (assets) as the overall amount of funds is constrained. However, if the funds constraint is viewed as nonbinding, then the amount lent
to borrower i can be expanded without affecting the amount lent to other
borrowers. In the KMV-type marginal risk contribution calculation, a
funding constraint is assumed to be binding:
Xi + Xj + ⋅⋅⋅ + Xn = 1
By comparison, in CreditMetrics, the marginal risk contributions are calculated assuming no funding constraint. For example, a financial organization can make a loan to a tenth borrower without reducing the loans
outstanding to the nine other borrowers.
Assuming a binding funding constraint, the marginal risk contribution (MRC) for the ith loan can be calculated as follows:
ULp =
冱 X 2i ⋅ UL2i + 冱 冱 XiXjULiULjρij
i=1 i=1
i ≠ 1
冱X =1
The marginal risk contribution can also be viewed as a measure of
the economic capital needed by the bank in order to grant a new loan to
the ith borrower, because it reflects the sensitivity of portfolio risk (specifically, portfolio standard deviation) to a marginal percentage change in
the weight of the asset. Note that the sum of MRCs is equal to ULp; consequently, the required capital for each loan is just its MRC scaled by the
capital multiple (the ratio of capital to ULp).133 CreditMetrics
In contrast to KMV, CreditMetrics can be viewed more as a loan portfolio
risk-minimizing model than a full-fledged MPT risk–return model. Returns on loans are not explicitly modeled. Thus, the discussion focuses on
the measurement of the VaR for a loan portfolio. As with individual loans,
two approaches to measuring VaR are considered:
Loans are assumed to have normally distributed asset values.
The actual distribution exhibits a long-tailed downside or
negative skew.
The normal distribution approach is discussed; this approach produces
a direct analytic solution to VaR calculations using conventional MPT
Portfolio VaR Under the Normal Distribution Model
In the normal distribution model, a two-loan case provides a useful benchmark. A two-loan case is readily generalizable to the N-loan case; that is,
the risk of a portfolio of N loans can be shown to depend on the risk of
each pair of loans in the portfolio.
To calculate the VaR of a portfolio of two loans, we need to estimate:
Credit Risk
The joint migration probabilities for each loan (assumed to be the
$100-million face value BBB loan discussed, and an A-rated loan
of $100 million face value)
The joint payoffs or values of the loans for each possible one-year
joint migration probability
Joint Migration Probabilities
Table 3-9 shows the one-year individual and joint migration probabilities
for the BBB and A loans. Given the eight possible credit states for the BBB
borrower and the eight possible credit states for the A borrower over the
next year (the one-year horizon), there are 64 joint migration probabilities.
The joint migration probabilities are not simply the additive product of
the two individual migration probabilities. These can be recalculated by
looking at the independent probabilities that the BBB loan will remain
BBB (0.8693) and the A loan will remain A (0.9105) over the next year. The
joint probability, assuming the correlation between the two migration
probabilities is zero, would be 0.8693 ⋅ 0.9105 = 0.7915 or 79.15 percent. The
joint probability in Table 3-9 is slightly higher, at 79.69 percent, because the
assumed correlation between the rating classes of the two borrowers is 0.3.
Adjusting the migration table to reflect correlations is a two-step
process. First, a model is required to explain migration transitions. CreditMetrics applies a Merton-type model to link asset value or return volatilT A B L E 3-9
Joint Migration Probabilities with 0.30 Asset Correlation
Obligor 1 (BBB)
Obligor 2 (A)
SOURCE: J. P. Morgan, CreditMetrics Technical Document, New York: J. P. Morgan, April 2, 1997, 38. Copyright © 1997 by J.
P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.
ity to discrete rating migrations for individual borrowers. Second, a model
is needed to calculate the correlations among the asset value volatilities of
individual borrowers. Similar to KMV, asset values of borrowers are unobservable, as are correlations among those asset values. The correlations
among the individual borrowers are therefore estimated from multifactor
models driving borrowers’ stock returns.
Linking Asset Volatilities and Rating Transitions
To see the link between asset volatilities and rating transitions, consider
Figure 3-30, which links standardized normal asset return changes (measured in standard deviations) of a BB-rated borrower to rating transitions.134
If the unobservable (standardized) changes in asset values of the
firm are assumed to be normally distributed, we can calculate how many
standard deviations asset values would have to have to move the firm
from BB into default. For example, the historic one-year default probability of this type of BB borrower is 1.06 percent. Using the standardized normal distribution tables, asset values would have to fall by 2.3 σ for the firm
to default. Also, there is a 1 percent probability that the BB firm will move
to a C rating over the year. Asset values would have to fall by at least 2.04σ
to change the BB borrower’s rating to C or below. There is a 2.06 percent
probability (1.06% + 1.00%) that the BB-rated borrower will be downgraded to C or below (such as D). The full range of possibilities is graphed
in Figure 3-30. Similar figures could be constructed for a BBB borrower, an
F I G U R E 3-30
Link Between Asset Value Volatility σ and Rating Transitions for a BB-Rated Borrower. (Source: Modified from J. P. Morgan, CreditMetrics Technical Document,
New York: J. P. Morgan, April 2, 1997, 87, 88, tables 8.4 and 8.5, chart 8.2. Copyright © 1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.)
probability, %
volatility σ
Credit Risk
T A B L E 3-10
Link Between Asset Value Volatility σ and Rating Transitions
for an A-Rated Borrower
probability, %
volatility σ
SOURCE: J. P. Morgan, CreditMetrics Technical Document, New York: J. P. Morgan, April 2, 1997, 87, table 8.4. Copyright ©
1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.
A borrower, and so on. The links between asset volatility and rating
changes for an A borrower are shown in Table 3-10.
From Figure 3-30, we can see that a BB-rated borrower will remain
BB as long as the standardized normal asset returns of the borrowing firm
fluctuate between −1.23 σ and +1.37 σ. The A borrower’s rating will remain unchanged as long as the asset returns of the firm vary between
−1.51 σ and +1.98 σ. Assume that the correlation p between those two
firms’ asset returns is 0.2 (to be calculated in more detail later).
The joint probability Pr that both borrowers will remain simultaneously in the same rating class during the next year can be found by integrating the bivariate normal density function as follows:
Pr(−1.23 < BB < 1.37, −1.51 < 1.98) =
冕 冕
−1.23 −1.51
f(ζ1ζ 2; ρ) ⋅ ζ1ζ 2 = 0.7365
where ζ1 and ζ2 are random, and ρ = 0.20.
In Equation (3.51), the correlation coefficient ρi is assumed to be
equal to 0.2. As described next, these correlations, in general, are calculated in CreditMetrics based on multifactor models of stock returns for the
individual borrower.135
Joint Loan Values
In addition to 64 joint migration probabilities (in this generic example), we
can calculate 64 joint loan values in the two-loan case, as shown earlier
(Table 3-9). The market value for each loan in each credit state is calculated
and discussed under Joint Migration Probabilities. Individual loan values
are then added to get a portfolio loan value, as shown in Table 3-11. Thus, if
T A B L E 3-11
Loan Portfolio Value: All 64 Possible Year-End Values for a Two-Loan Portfolio
Obligor 1 (BBB)
Obligor 2 (A)
J. P. Morgan, CreditMetrics—Technical Document, New York: J. P. Morgan, April 2, 1997, 12. Copyright © 1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of
RiskMetrics Group, Inc.
Credit Risk
both loans get upgraded to AAA over the year, the market value of the loan
portfolio at the one-year horizon becomes $215.96 million. By comparison,
if both loans default, the value of the loan portfolio becomes $102.26 million.
With 64 possible joint probabilities and 64 possible loan values, the
mean value of the portfolio and its variance are as computed in Equations
(3.52) and (3.53):
Mean = p1 ⋅ V1 + p2 ⋅ V2 + ⋅⋅⋅ + p64 ⋅ V64 = $213.63 million
Variance = p1 ⋅ (V1 − mean)2
+ p2 ⋅ (V2 − mean)2 + ⋅⋅⋅
+ p64 ⋅ (V64 − mean)2
= $11.22 million
Taking the square root of the solution to Equation (3.53), the σ of the
loan portfolio value is $3.35 million and the VaR at the 99 percent confidence
level under the normal distribution assumption is 2.33 ⋅ $3.35 = $7.81 million.
Comparing this result of $7.81 million for a face-value credit portfolio of $200 million with the 99 percent VaR-based capital requirement of
$6.97 million (for the single BBB loan of $100 million face value as derived
earlier, we can see that although the credit portfolio has doubled in face
value, a VaR-based capital requirement (based on the 99th percentile of
the loan portfolio’s value distribution) has increased by only $0.84 million
($7.81 million − $6.97 million). The reason for this low increase in VaR is
portfolio diversification. A correlation of .3 between the default risks of the
two loans is built into the joint transition probability matrix in Table 3-11.
Portfolio VaR Using the Actual Distribution
The capital requirement under the normal distribution is likely to underestimate the true VaR at the 99 percent level because of the skewness in the
actual distribution of loan values. Using Table 3-9 in conjunction with
Table 3-11, the 99 percent (worst-case scenario) loan value for the portfolio
is $204.40 million.136 The unexpected change in value of the portfolio from
its mean value is $213.63 million − $204.40 million = $9.23 million. This is
higher than the capital requirement under the normal distribution discussed previously ($9.23 million versus $7.81 million); however, the contribution of portfolio diversification is clear. In particular, the regulatory
capital requirement of $9.23 million for the combined $200-million facevalue portfolio can be favorably compared to the $8.99 million for the individual BBB loan of $100 million face value.
Parametric Approach with Many Large Loans
The normal distribution approach can be enhanced in two ways:
The first way is to keep expanding the loan joint transition
matrix, directly or analytically computing the mean and standard
deviation of the portfolio. However, this rapidly becomes
computationally difficult. For example, in a five-loan portfolio,
there are 81 possible joint transition probabilities, or over 32,000
joint transitions.
The second way is to manipulate the equation for the variance of
a loan portfolio. It can be shown that the risk of a portfolio of N
loans depends on the risk of each pairwise combination of loans
in the portfolio as well as the risk of each individual loan. To
consistently estimate the risk of a portfolio of N loans, only the
risks of subportfolios containing two assets need to be calculated.
CreditMetrics uses Monte Carlo simulation to compute the distribution of loan values in the large sample case in which loan values are not
normally distributed. Consider the portfolio of loans in Table 3-12 and the
correlations among those loans (borrowers) in Table 3-13. For each loan,
20,000 (or more) different underlying borrower asset values are simulated,
based on the original rating of the underlying loan, the joint transition
probabilities, and the historical correlations among the loans.137 The loan
(or borrower) can either stay in its original rating class or migrate to another rating class. Each loan is then revalued after each simulation and rating transition. Adding across the simulated values for the 20 loans
produces 20,000 different values for the loan portfolio as a whole. Based
on the 99 percent worst-case scenario, a VaR for the loan portfolio can be
calculated as the value of the loan portfolio that has the 200th worst value
out of 20,000 possible loan portfolio values.
In conjunction with the mean loan portfolio value, a capital requirement can be derived. The CreditMetrics portfolio approach can also be
applied to calculation of the marginal risk contribution for individual
loans. Unlike the KMV approach, funds are considered as being flexibly
adjustable to accommodate an expanded loan supply, and marginalmeans loans are either granted or not granted to a borrower, rather than
making an incremental amount of new loans to an existing borrower.
Table 3-14 demonstrates the stand-alone and marginal risk contributions of 20 loans in a hypothetical loan portfolio based on a standard deviation measure of risk σ. The stand-alone columns reflect the dollar and
percentage risk of each loan, viewed individually. The stand-alone percentage risk for the CCC-rated asset (number 7) is 22.67 percent, and the
B-rated asset (number 15) is 18.72 percent. The marginal risk contribution
columns in Table 3-14 reflect the risk of adding each loan to a portfolio
containing the remaining 19 loans (the standard deviation risk of a 20-loan
Credit Risk
T A B L E 3-12
Example Portfolio
Credit asset
Principal amount, $
Maturity, years
Market value, $
SOURCE: J. P. Morgan, CreditMetrics—Technical Document, New York: J. P. Morgan, April 2, 1997, 121. Copyright © 1997
by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.
portfolio minus the standard deviation risk of a 19-loan portfolio). Interestingly, Table 3-14, on a stand-alone basis, Asset 7 (CCC) is riskier than
Asset 15 (B), but when risk is measured in a portfolio context (by its marginal risk contribution), Asset 15 is riskier. The reason can be seen from the
correlation matrix in Table 3-13, where the B-rated loan (Asset 15) has a
“high” correlation level of 0.45 with Assets 11, 12, 13, and 14. By comparison, the highest correlations of the CCC-rated loan (Asset 7) are with Assets 5, 6, 8, 9, and 10, at the 0.35 level.
One policy implication is immediate and is shown in Figure 3-31,
where the total risk (in a portfolio context) of a loan is broken down into two
T A B L E 3-13
Asset Correlations for Example Portfolio
J. P. Morgan, CreditMetrics—Technical Document, New York: J. P. Morgan, April 2, 1997, 122. Copyright © 1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.
Credit Risk
T A B L E 3-14
Standard Deviation of Value Change
Absolute, $
Credit rating
Absolute, $
SOURCE: J. P. Morgan, CreditMetrics—Technical Document, New York: J. P. Morgan, April 2, 1997, 130. Copyright © 1997
by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.
components: (1) its percentage marginal standard deviation (vertical axis)
and (2) the dollar amount of credit exposure (horizontal axis). We then have:
Total risk of a loan
= marginal standard deviation, % × credit exposure, $ (3.54)
For the 13-rated loan the standard deviation results in a risk of:
$270,000 = 8.27% × $3,263,523
F I G U R E 3-31
Marginal standard deviation, %
Credit Limits and Loan Selection in the CreditMetrics Framework. (Source: Modified from J. P. Morgan, CreditMetrics Technical Document, New York: J. P. Morgan,
April 2, 1997, 131. Copyright © 1997 by J. P. Morgan & Co., Inc., all rights reserved. Reproduced with permission of RiskMetrics Group, Inc.)
Asset 15
Asset 7
Asset 16
Asset 9
Asset 18
Credit exposure, $M
Also plotted in Figure 3-32 is an equal risk isoquant of $70,000. Suppose managers wish to impose a total credit risk exposure limit of $70,000
on each loan measured in a portfolio context. Then Asset 15 (the 13-rated
loan) and Assets 16 and 9 are obvious outliers. One possible alternative
would be for the financial institution to sell Asset 15 to another institution,
or to swap it for another B-rated asset that has a lower correlation with the
other loans (assets) in the institution’s portfolio. In doing so, its expected
returns may remain (approximately) unchanged, but its loan portfolio risk
is likely to decrease due to an increased benefit from diversification. Alternative Portfolio Approaches
CreditPortfolioView and CreditRisk† can only be considered partial MPT
models, similar to CreditMetrics, because the returns on loans and the
loan portfolio are not explicitly modeled.
The role of diversification in CreditPortfolioView is obvious in the
context of the macroshock factors (or unsystematic risk factors) U and V
(see Section, which drive the probability of borrower default over
time. As portfolio diversification increases (e.g., across countries in the
CreditPortfolioView model), the relative importance of unsystematic risk
to systematic risk will shrink, and the exposure of a loan portfolio to shocks
Credit Risk
will shrink. In the context of the Monte Carlo simulations of the model, the
99 percent worst-case loss for an internationally well diversified portfolio
is likely to be less pronounced (other things being equal) than that for a
concentrated one-country or industry-specialized loan portfolio.
In CreditRisk†, two model cases have to be distinguished. In Model 1
(see Section 3.8.9), two sources of uncertainty can be identified: the frequency described by the Poisson distribution of the number of defaults
(around a constant mean default rate), and the severity of losses (variable
across loan exposure bands). Because the Poisson distribution implies that
each loan has a small probability of default and that this probability is independent across loans, the correlation of default rates is, by definition, zero.
In Model 2, however, where the mean default rate itself is variable
over time (described with a gamma distribution), correlations are induced
among the loans in the portfolio because they show varying systematic
linkages to the mean default rate movements. As discussed in Section
3.8.10, the movement in the mean default rate can be modeled in terms of
factor sensitivities to different independent sectors (which could be countries or industries). For example, a company’s default probability may be
sensitive to both a U.S. factor and a UK factor. Given this trait, the default
correlations in CreditRisk† are shown to be equal to:
ρAB = (mAmB)1/2 冱 θAkθBk ᎏᎏ
冢 冣
ρAB = default correlation between borrowers A and B
mA = mean default rate for Type-A borrower
mB = mean default rate for Type B borrower
θA = allocation of borrower A’s default rate volatility across N
θB = allocation of borrower B’s default rate volatility across N
(σk/mk)2 = proportional default rate volatility in sector k
Table 3-15 demonstrates an example of Equation (3.55) where each of
the two borrowers is sensitive to one economywide sector only (θAk = θBk = 1),
and σk/mk = 0.7 is set at an empirically reasonable level. As can be seen from
Table 3-15, as the credit quality of the borrowers declines (i.e., mA and mB get
larger), correlations increase. Nevertheless, even in the case in which individual mean default rates are high (mA = 10 percent and mB = 7 percent), the
correlation among the borrowers is still quite small (in this case, 4.1 percent).
Another issue to discuss is correlations derived from intensity-based
models. The correlations among default rates reflect the effect of events in
inducing simultaneous jumps in the default intensities of obligors. The
causes of defaults themselves are not modeled explicitly. However, what
T A B L E 3-15
Relationship Between Mean Default Rates
and Default Correlations
σk /mk
Credit Suisse First Boston, CreditRisk+, technical document,
London/New York, October 1997. Reproduced with permission of Credit Suisse
First Boston (Europe) Ltd.
are modeled are various approaches to default-arrival intensity that focus
on correlated times to default. This allows the model to answer questions
such as the worst week, month, year, and so on, out of the past N years, in
terms of loan portfolio risk. The worst period is derived when correlated
default intensities were highest (defaults arrived at the same time). With
joint credit events, some of the default intensity of each obligor is tied to
such an event with some probability.138
3.9.7 Differences in Credit versus
Market Risk Models
In analyzing the applicability of regulatory requirements to the credit risk
issue, it appears that qualitative standards will play a similarly important
role in the assessment of the accuracy of credit risk models and the credit
process (such as management oversight). However, the application of
quantitative standards to credit risk models is likely to be more difficult
than for market risks for the following reasons:
Data limitation and data integrity appear to be major hurdles in the
design and implementation of credit risk models. Most credit
instruments are not marked to market. The statistical evidence for
credit risk models does not derive from a statistical analysis of
prices; the comprehensive historical basis is not comparable to
that for market risks. The scarcity of the data required for
modeling credit risk also stems from the infrequent nature of
default events and the longer-term time horizons used in
measuring credit risk. The parameterization of credit risk models
Credit Risk
requires a more in-depth understanding of the model’s sensitivity
to structural assumptions and parameter estimates, requiring the
use of simplifying assumptions, parameters, and proxy data.
Validation and verification of credit risk models are also
fundamentally more difficult than the backtesting procedure
used for market risk models. Based on the frequency of the data
available, market risk models typically employ a horizon of a few
days, whereas credit risk models generally rely on a time frame of
one year or more. Longer holding periods, combined with the
higher target loss quantiles used in credit risk models, present
design problems in assessing the accuracy of the models. A
quantitative standard for the validation of the accuracy of models
similar to that presented in the Market Risk Amendment would
require an impractical number of years of data, spanning
multiple credit cycles.
The segment of an institution’s banking book concerned with
credit risk exposures and the length of the time horizon of such
products are much greater than those of the trading books.
Hence, errors in measuring credit risk are more likely to affect the
assessment of the bank’s overall soundness. It appears more
likely that losses can accumulate over time unnoticed in the
banking book, as it is not marked to market on a regular basis.
3.10.1 Background
A critical issue for financial organizations and regulators is the validation
and predictive accuracy of internal models. In the context of market models, this issue has led to numerous efforts to backtest models to ascertain
their predictive accuracy. Under the current BIS market risk–based capital
requirements, a financial organization must validate the accuracy of its internal market models through backtesting over a minimum of 250 past
days if they are used for capital requirement calculations. If the predicted
VaR errors for those 250 days are outside a given confidence level (i.e., risk
is underestimated on too many days), penalties are imposed by regulators
to create incentives for bankers to improve the models.139
It can be argued, however, that backtesting over a 250-day time horizon is not enough, given the high standard-deviation errors that are likely
to be involved if the period is not representative. To reduce errors of this
type, suggestions have been made to increase the number of historical
daily observations over which a backtest of a model is conducted. For example, a horizon of at least 1000 past daily observations is commonly be-
lieved to be adequate to ensure that the period chosen is representative in
terms of testing the predictive accuracy of any given model. However,
even for traded financial assets such as currencies, a period of 1000 past
days requires going back in time more than four years and may involve
covering a wide and unrepresentative range of foreign-exchange regimes,
as such a horizon may include structural changes.
The key measure of the usefulness of internal credit risk models is their
predictive ability. Tests of predictive ability, such as backtesting, are difficult
for credit risk models because of the lack of the following requirements:
Sufficiently long time-series data. Given a large and representative
(in a default risk sense) loan portfolio, it is possible to stress-test
credit risk models by using cross-sectional subportfolio sampling
techniques that provide predictive information on average loss
rates and unexpected loss rates.
Comparability of conditioning variables from model to model. The
predictive accuracy, in a cross-sectional sense, of different models
can be used to select different models. In the future, wider-panel
data sets, and time series of loan loss experience, are likely to be
developed by financial institutions and consortiums of banks
(e.g., the British Bankers’ Association). The credit risk models are
used at the beginning of such an exercise, and it is important to
note that, to be really useful, these loan portfolio experience data
sets should include not only loss experience but also the
conditioning variables that the different models require (e.g.,
recoveries, loan size, ratings, and interest rates).
3.10.2 Credit Risk Models and Backtesting
To appropriately backtest or stress-test market risk models, 250 observations are required. But it is unlikely that a bank would be able to provide
anywhere near that many past observations. With annual observations
(which are the most likely to be available), a bank might be able to provide
only a fraction of the required historical observations, severely limiting
the institution to a capacity to perform only time-series backtesting similar to that which is currently available for market risk models.140
3.10.3 Stress Testing Based on Time-Series
Versus Cross-Sectional Approaches
Recent studies from Granger and Huang141 (at a theoretical level), and
Carey142 and Lopez and Saidenberg143 (at a simulation and empirical level),
provide evidence that stress tests similar to those conducted across time for
market risk models can be conducted using cross-sectional or panel data for
Credit Risk
credit risk models. In particular, suppose that in any given year a bank has
a sample of N loans in its portfolio, where N is sufficiently large. By repeated
subsampling of the total loan portfolio, it is possible to generate a cross-sectional distribution of expected losses, unexpected losses, and the full probability density function of losses. By comparing cross-sectional subportfolio
loss distributions with the actual full-portfolio loss distribution, it is possible to estimate the predictive accuracy of a credit risk model. If the model is
a good predictor—and thus the backtesting results should support this
statement—the mean average loss rate and the mean 99th percentile loss
rate from a high number of randomly drawn subportfolios of the total loan
portfolio (e.g., 10,000) should be statistically close to the actual average and
99th percentile loss rates of the full loan portfolio experienced in that year.144
A number of statistical problems arise with cross-sectional stress
testing, but these are similar to those that arise with time-series stress testing (or backtesting):
The first problem, and perhaps the most critical, is ensuring the
representative nature of any given year or subperiod selected to
determine statistical moments such as the mean (expected) loss
rate and the 99 percent unexpected loss rate. Structural changes
in the market can make past data invalid for the prediction of
future losses. The emergence of new credit instruments, changes
in the fiscal behavior of the government, and legal or regulatory
changes regarding debt and equity treatment, tax law, and so
forth can impact the way a model reflects systematic versus
unsystematic risk factors. This suggests that some type of
screening test needs to be conducted on various recession years
before a given year’s loss experience is chosen as a benchmark for
testing predictive accuracy among credit risk models and for
calculating capital requirements.145
The second problem is the effect of outliers on simulated loss
distributions. A few extreme outliers can seriously affect the
mean, variance, skew, and kurtosis of an estimated distribution,
as well as the correlations among the loans implied in the
portfolio. In a market risk model context, it can be shown that
only 5 outliers out of 1000 observations, in terms of foreign
currency exchange rates, can have a major impact on estimated
correlations among key currencies.146 When applying this issue to
credit risk, the danger is that a few major defaults in any given
year could seriously bias the predictive power of any crosssectional test of a given model.
The third problem is that the number of loans in the portfolio has
to be large; therefore, the data sample has to be very large. It will
be big enough only in the case of a nationwide database.
For example, Carey’s sample is based on 30,000 privately placed
bonds held by a dozen life insurance companies from 1986 to 1992, a period during which more than 300 credit-related events (defaults, debt restructurings, and so on) occurred for the issuers of the bonds.147 The
subsamples chosen varied in size; for example, portfolios of $0.5 to $15 billion, containing no more than 3 percent of the bonds of any one issuer.
Table 3-16 shows simulated loss rates from 50,000 subsample portfolios
drawn from the 30,000-bond population. Subportfolios were limited to $1
billion in size.
Table 3-16 compares Monte Carlo estimates of portfolio loss rates at
the mean and at various percentiles of the credit loss rate distribution,
when Monte Carlo draws are limited to the good years, 1986 to 1989; the
bad years, 1990 to 1992; and the worst year, 1991. All drawn portfolios
are $1 billion in size. The two panels, each with three rows, report results
when all simulated portfolio assets are investment grade and below
investment grade (rated <BBB), respectively. An exposure-to-oneborrower limit of 3 percent of the portfolio size was enforced in building
simulated portfolios. The results in each row are based on 50,000 simulated portfolios.
T A B L E 3-16
Loss Rate Distribution When Monte Carlo Draws Are from Good Versus Bad Years
< BBB, %
Simulated Portfolio Loss Rate, %
Loss Distribution Percentile
Very bad:
Good: 1.73
Very bad:
Mark Carey, “Credit Risk in Private Debt Portfolios,” Journal of Finance (August 1998), 1363–1387. Reproduced with
permission of Blackwell Publishing.
Credit Risk
The loss rates vary by year. In 1991, which was the trough of the last
U.S. recession, 50,000 simulated portfolios containing <BBB bonds produced a mean 99 percent loss rate of 8.04 percent, which is quite close to
the BIS 8 percent risk-based capital requirement. However, note that in relatively good years (e.g., 1986 to 1989), the 99 percent loss rate was much
lower: 5.11 percent.
Credit Lines Description
Credit lines originate when a bank extends credit to a borrower with a
specified maximum amount and a stated maturity. The borrower then
draws and repays funds through the facility in accordance with its requirements. Lines of credit are useful for short-term financing of working
capital or seasonal borrowings. A commitment fee is usually charged on
the unused portion. These loans are often unsecured but may be collateralized by accounts receivable, securities, or inventory. The contractual
profile depends on the risks involved and the experience of the bank with
the specific client. Firms engaged in manufacturing, distribution, retailing, and the service sector often use lines of credit to finance short-term
working-capital needs. Inherent Risk Types
As with all credit, the primary risk is that the borrower will default and be
unable to repay the principal amount amortization and interest outstanding at any point in time. Lines-of-credit facilities are exposed to an element
of contingent principal risk in that the bank generally has a contractual
commitment to lend additional funds on demand. Depending on the contractual profile, market risk through interest-rate fluctuations might affect
the profitability of a credit line. Variable-interest payments from the borrower to the bank will change over time, depending on actual interest
rates and the reset dates. Quantification of Credit Risks
The bank’s exposure on a line-of-credit facility consists of the following
Outstanding principal amount (less amortization paid)
Accrued interest outstanding
Credit equivalent exposure from the remaining commitment to
lend additional funds on demand (which can be quantified as the
remaining amount of the maximal credit level multiplied by the
probability of drawdown by the borrower)
The next step is to assess the borrower’s total exposure. The bank has
to determine the likelihood that the borrower will default. To collateralize
the borrower’s credit, the bank has to value the net realizable assets. All
these factors are used to quantify the overall credit exposure and serve as
a basis to calculate the provisioning. Exposure to Market Risks
The bank has a market risk if the interest payments from the borrower to
the bank are based on variable rates. The bank is thus exposed to changes
in the level and the term structure of interest rates.
3.11.2 Secured Loans Description
The less creditworthy a potential borrower is, the more likely it becomes
that a bank will request some form of collateral in order to minimize its
loss exposure. Securititization is regarded as characteristic of any type of
credit, rather than a credit category of its own. Banks analyze their loan
portfolios by reviewing the proportion of secured (collateralized) credits
to the entire portfolio balance.
Loan security is usually not an activity performed expressly to generate business activity and profit. Maintenance, administration, and liquidation of collaterals are in fact often expensive, time consuming, and
therefore unprofitable for the foreclosing institute. In many cases, the
bank lacks the expertise to seize assets which have to be liquidated. It is
more useful to sell the security. Considerations such as insurance, legal
liability, and the cost of maintenance can be critical when deciding
whether to repossess collateral.
Most credit security is formulated in some kind of fixed or floating
claim over specified assets or a mortgage interest in property. Table 3-17
describes some common forms of credit security. Inherent Risk Types
As with all loans, the lender is exposed to borrower default. It is the primary risk associated with loans—the risk that the borrower will be unable
to meet the obligation to repay the principal and interest outstanding at
any point in time. Banks collateralize loans to reduce their exposure to loss
due to borrower default.
Liquidation of collaterals is usually not a profitable business for a
bank. Rising interest rates increase the risk of default, as the outstanding
interest might be higher than the financing power of the borrower. Decreasing market values of property increase the collateralized part of the
loans and increase the risk that the bank will have higher loss exposures in
case of borrower default.
Credit Risk
T A B L E 3-17
Common Forms of Credit Security
Loan Security
A lien is a right to retain someone’s property until a debt due
from the borrower has been repaid (the borrower and owner
need not be identical). Banks require that liens used as security
be in writing and refer specifically to the property under lien.
Depending on local regulations and location of the property, the
lien has to be officially approved by a notary and recorded in
public records in order to be enforceable.
A mortgage is a lien on real property. The mortgage does not
affect the rights of ownership, as they do not pass to the bank.
An assignment is a transfer by a borrower of the right to receive
a benefit from a third-party debtor. Usually the transfer is money
or securities to be assigned as receivables to the bank as
security for the loan.
Hypothecation is a form of direct security involving only indirect
legal title. This approach is chosen when it is not practical for the
bank to take actual physical possession of either the goods or
related title documents. The bank has a claim over items which it
neither controls nor owns.
A guarantee is a common form of indirect security involving the
acceptance by a third party of responsibility for the debts or
defaults of the borrower.
A pledge is a direct security based on an express agreement that
gives a bank possession but not ownership of specific goods or
title documents. Quantification of Credit Risks
The quantification of credit risks can be considered the outcome of the
process of assessing the risk exposure to a bank’s secured lending. The
first step is to classify the loans within the bank’s credit analysis system.
The bank will establish a limit up to which a secured loan can be granted.
If the risk of default is determined to be substantial because of deterioration in the borrower’s financial condition, poor payment history, decreased asset values, and the like, the bank must take action and prepare
for liquidation of the collateral as the ultimate step.
Often the term net realizable value is used for the liquidation value.
The net realizable value consists of the following components:
The current market value of the collateral
A provision for all costs of administration and maintenance from the
time the bank takes possession of the collateral until the time of sale
A reserve provision for potential decline in market value from the
time the bank takes possession of the collateral until the time of
A provision for insurance premiums
A provision for selling costs
Claims by other creditors (lenders) whose security interest in the
collateral are ranked higher than the bank’s ranking
Revenues to be generated prior to disposing of the collateral
The realization of the net realizable value is generally a subjective and
complex process—particularly the liquidation of collaterals where no liquid market exists (real estate in specific geographic areas, used manufacturing equipment, etc.).
The calculation of capital adequacy for credit risks uses different risk
weightings. Specifically, loans that are fully collateralized by government
securities or guaranteed by the government have a 0 percent weighting.
Loans to private persons for purchase of a residence fully secured by a
mortgage will have a weighting of 50 percent or more. Exposure to Market Risks
Rising interest rates increase the risk of default, as the outstanding interest
might be higher than the financing power of the borrower. Specifically, for
loan contracts with a floating interest rate, increasing interest rates will be
rolled over to the borrower at the reset dates. Contracts with a fixed interest rate might be foreclosed, which exposes the borrower to a reinvestment risk at a higher interest-rate level. Decreasing market values of
property increase the collateralized part of the loans and increase the risk
that the bank will have higher loss exposures in case of borrower default.
3.11.3 Money Market Instruments Description
The traditional classification of securities separates the money market instruments and the capital market instruments. The money market includes
short-term, marketable, liquid, low-risk debt securities. Money market instruments are sometimes called cash equivalents because of their safety and
liquidity. They are usually highly marketable and trade in large denominations; therefore, they are beyond the reach of individual investors. Table
3-18 lists instruments commonly used as money market instruments. They
have different profiles (legal structure, secured/unsecured, etc.) and the
degree of their activity in the market differs, but there are also considerable
similarities in their applications.
A bank using money market instruments for both borrowing and
lending would pursue some or all of the following objectives:
T A B L E 3-18
Common Forms of Money Market Securities
Money Market Instrument
Interbank placement
The interbank placement market is extremely liquid and active. It enables banks and other financial institutions to
raise short-term funding or to place excess funds. Placements on a call basis are possible, from one day (overnight)
to up to five years.
The interbank placement market developed from the eurocurrency market. This market originally developed following the
placement of U.S. dollars outside the United States; it first became the eurobond market, based on these eurodollars.
Subsequently, it moved into shorter maturities in the eurocurrency market, including currencies such as sterling, euros,
and Swiss francs. It now represents an international money market outside clear national boundaries, covering all
financial centers worldwide, 24 hours a day. The interbank placement market is a global market not linked to a specific
time zone. For international banks and institutions, it is possible to raise and place funds whenever required and to
globally manage money market portfolios on a location-by-location basis. The portfolio can be transferred to the next
location for ongoing management of the positions currently in the portfolio.
Eurocurrency in the London market is usually linked to the LIBOR; the participants quote the rate at which they are
willing to accept (borrow) or place (lend) funds. The spread between the bid and the ask reflects the liquidity of the
market and the credit quality of the counterparty.
Major banks have also begun to develop instruments with similar characteristics for foreign issuers, in different
currencies. Large multinational firms offer these instruments to finance their short debts.148
Banker’s acceptance
Similar to letters of credit, banker’s acceptances are securities that are written when a bank places itself between the
borrower and the investor and accepts responsibility for paying the loan. This shields the investor from the risk of
default. A banker’s acceptance is often preceded by a written promise from the lending bank that it will make the loan.
The lending bank does not actually accept the banker’s acceptance until the borrower takes down the loan. Later, if
the lending bank wants to withdraw the money it has invested in the loan before the loan expires, the bank can sell the
banker’s acceptance to another investor. Banker’s acceptances may be resold to any number of other investors before
the loan is repaid. There is an active secondary market in these debts. Any investor who buys a banker’s acceptance
can collect the loan on the date it is scheduled to be repaid.
Banker’s acceptances are among the oldest money market securities. They are typically used to expedite foreign
trade by financing accounts receivable between buyers and sellers from different countries. Large international banks
create banker’s acceptances for the interest rates on loans, with a provision depending on the creditworthiness.
T A B L E 3-18
Common Forms of Money Market Securities (Continued )
Money Market Instrument
Certificates of deposits
Certificates of deposit (CDs) are an important source of medium-term funds. They are negotiable instruments issued
by banks for deposits placed with them for a fixed period of time. CDs can be traded in an active secondary market.
This liquidity gives CDs an advantage through a rate of interest which is slightly lower than that of an equivalent-time
deposit in the interbank market. CDs can have fixed interest rates or floating and variable rates. Rates are normally
priced as a spread over LIBOR.
Repo agreements
Sale and repurchase agreements are short-term loans secured by collateral in the form of securities. A repo
agreement consists of the sale of the underlying securities for immediate cash settlement with a simultaneous
agreement to repurchase the underlying securities at a higher price at a later date. The price difference between the
spot and future price represents an interest charge for the use of cash received or lent during the time horizon of the
contract. The counterparty to a repo transaction engages in a reserve repo, which is the purchase of the securities
against cash settlement and simultaneous agreement to sell them at a higher price in the future.
This is a particularly common interbank mechanism for transferring short-term funds from banks with excess funds to
those with short-term requirements.
For lenders of funds, it is important to reduce risk by ensuring that the securities purchased are received and held
throughout the life of the transaction (usually through a depository). The borrower cannot use the same securities for
another transaction. In addition, the borrower and lender have to agree on the initial price and must monitor
subsequent price movements. In the event of falling market prices, the lender will require additional collateral to cover
the initial transaction amount. In the event of increased market prices, the borrower will recall excess collateral. The
collateral deposited is kept in balance with the initial transaction amount, as any unbalance hurts profitability and
increases risk for either the borrower or the lender.
Commercial paper
Commercial paper consists of unsecured promissory notes with a fixed maturity. These notes are backed only by the
credit rating of the issuing corporation and are therefore normally issued only by banks and other businesses with
high credit ratings. Commercial paper is usually issued in bearer form and on a discounted basis. Commercial paper
issuers typically maintain open lines of bank credit sufficient to pay back all of their outstanding commercial paper at
maturity. They issue commercial paper only because that type of credit is quicker and easier to obtain than bank
loans. The credit ratings of most commercial paper issuers are so high that the so-called prime (that is, highest-quality
credit rating) commercial paper interest rate is essentially a riskless rate of interest, matching the yields on negotiable
CDs and banker’s acceptances.
Credit Risk
Generating arbitrage profits between the money markets and
other related business activities (e.g., futures, swaps, and foreign
Generating profits from dealing in money market instruments
and from taking positions in interest-rate positions
Generating profits from market making (dealing) from the
bid–ask spread of interest-rate positions
Optimizing the use of capital by gearing the balance sheet to the
required level
Money market activities fund other business activities, manage liquidity, and define interest rates on leading transactions. These activities
are centrally undertaken in the treasury department. Many banks generate more profit from nonoperative treasury activities by utilizing the
money markets to generate profits from arbitrage between the markets
and other products, by taking a view on future developments (speculation), or by dealing as a market maker in specific positions. Each of these
means of participation in the money market generates risk exposure for
the bank. Inherent Risk Types
The money markets are highly liquid, and the credit risk of the counterparties is considered low. Apart from credit and market risk, settlement
risk can be substantial and critical, as the volume of money market activities is high. The settlement of these transactions is therefore critical. But as
the range of participants in the money market business is known, and supervision of the counterparties is required by regulation, the remaining
counterparty exposures are reduced to a shorter time horizon than in the
capital market. Quantification of Credit Risks
The primary risk is the risk of borrower default. As most of the players in
the money markets are banks, the effect of such a default would be a significant change in the bank’s liquidity management as a result of the withdrawal of a large portion of the bank’s deposit base or funding sources. A
substantial default would affect the banking system through a ripple effect of defaults because of the substantial interbank deposit activity.
Listing authorized institutions with which the funds may be placed
and limiting the amount of deposits or bank assets which may be placed
with specific institutions reduces the counterparty risk. Approval for a
counterparty to become an authorized institution is usually regulated.
One key consideration is the institution’s credit rating, as determined internally or externally.
238 Exposure to Market Risks
Money markets are highly liquid, as they serve to transfer funds from institutions that have excess funds to institutions that need additional
funds. As this market acts globally, 24 hours a day, money market interest
rates reflect all information in the market. Changes in expectations regarding inflation have an immediate impact, and interest rates change almost simultaneously with the revelation of new information. The steady
flow of information continuously changes the shape and level of interest
rates, and therefore the pricing and valuation of money market positions,
hedges, and arbitrage strategies as well.
3.11.4 Futures Contracts Description
The futures contract calls for delivery of an asset or its cash value at a specified delivery or maturity date for an agreed-upon price, called the futures
price, to be paid at contract maturity. The long position is held by the investor who commits to purchasing the commodity on the delivery date.
The counterparty who takes the short position commits to delivering the
commodity at contract maturity. The terms and conditions of a futures
contract are standardized depending on the future’s exchange. Quantity,
grade, or type of commodity, currency, or financial instrument at a specified future date and a specified price are set and regulated by the terms of
the futures exchange where the future’s instrument is traded. The terms
include the details of the contract type, settlement, and margin requirement. Most of the basic principles are valid for the different futures exchanges and contract types.
Financial futures include stock indexes, currencies, interest-rate instruments, commodity indexes, and so forth. Futures contracts are based
on specific financial instruments—for example, the futures contract on
U.S. Treasury obligations is based on the standard contract amount of
$100,000 used by the Chicago Board of Trade (CBOT). An investor who
sells such a contract to hedge a portfolio has an obligation to sell the Treasury obligation (i.e., deliver cash) at a future date at a price agreed on at
the time of the contract trade. Other futures contracts, such as currency futures, are based on a specific amount of one currency valued against another currency at a predetermined date in the future at a price agreed on
at the time of the contract. For example, London International Financial
Futures Exchange (LIFFE) is based on standardized contracts in sterling
against dollars in increments of £25,000 each. Like currency futures contracts, forward contracts are made in advance of delivery, but they differ
from futures in several respects:
A forward contract is a private agreement between two parties; it
is not created and traded on a standardized exchange.
Credit Risk
A futures contract can be closed out without delivery, while the
forward contract requires delivery and can not be resold, since
there is no secondary market.
Futures have margins, requiring daily realization of profits and
losses. Forward contracts realize profits and losses at delivery only.
A futures contract requires a deposit of an initial margin at the clearinghouse that handles the two sides of the transaction. For any transaction,
two contracts are written: one between the buyer and the clearinghouse,
and one between the seller and the clearinghouse. At the end of each trading day, the positions are compared to the market value, and as prices
change, the proceeds accrue to the trader’s margin account immediately.
This daily settling is called marking to market. If an investor accrues sustained losses from daily marking to market, the margin account may fall
below a critical value, called the maintenance or variation margin. Once the
value of the margin account falls below this value, the investor receives a
margin call to transfer new funds into the account, or the broker will close
out enough of the position to meet the required margin for that position.
This procedure safeguards the position of the clearinghouse. Marking to
market is the major means of limiting risk. Initial margins may be less than
1 percent of the face value of the contract and may have no significant impact on the accounting. But the daily marking to market ensures that the
profits and losses from futures are calculated and booked daily. Through
this procedure, all contracts are standardized in terms of the other party, as
well as in terms of size and delivery date. To cancel a position, the investor
simply has to reverse the trades by selling contracts previously bought.
This creates a highly liquid market in standardized instruments.
A futures contract obliges the long position to purchase the asset at the
futures price. In contrast, the call option conveys the right to purchase the
asset at the exercise rate. The purchase will be made only if it yields at profit.
Futures can be used for different purposes:
Hedging. Buying or selling a future can be used to hedge the
underlying position. Within a very short time a hedge can be
built up to lengthen or shorten the duration of a portfolio, so the
downside of an equity portfolio can be protected by selling a
corresponding equity futures index, and so forth.
Position generation. Exposures to markets, segments, and so
forth can be built up with a fraction of the face value of the
futures contract. Instead of buying the underlying instruments,
only the initial margin is required to generate the equivalent
exposure. It is an efficient way to generate exposure if direct
exposure through buying the underlying instrument is not
desired for any reason.
Arbitrage trading. Options can be traded by buying and selling
futures that appear to be over- or underpriced compared to
similar products or markets issued by different counterparties,
using different valuation models to generate an arbitrage position.
Asset–option and option–option trading. Options can be traded by
buying and selling options to combine these options with each
other or in combination with underlying instruments to produce
structured products with risk–reward profiles different from
those of the underlying instrument or the individual option.
Speculation. Speculation can be regarded as a special case of
trading with open futures positions. The speculator expects that
the actual future movements of the underlying instrument or the
individual option will differ from the expected movements
(expected parameters) inherent in the current futures price. The
difference between the cash and futures prices is known as the
basis. Speculators take direct open positions (i.e., selling futures
without the underlying instrument and expecting the instrument
price to decrease). Inherent Risk Types
Credit risk is limited to margin amounts, or marking to market. Payments
due to or from the broker, or to the clearinghouse, do not include the overall amount of the underlying instruments. The futures contract has a symmetrical risk–reward profile for both counterparties.
Market risks have an important influence on the overall risk exposure of futures, as most of the input variables (currencies, interest rates,
equity prices, etc.) are market risk factors. Quantification of Credit Risks
The credit risk of futures contracts can be categorized as follows:
Credit risk arising from managing margin accounts.
Credit risk when a counterparty is unable to deliver the contract
(or its cash equivalent) or to meet the required margin call. In
such cases, the futures contract can not be covered at current
market rates, and a loss is incurred, which should not normally
exceed the margin amount.
The risk involved with exchange-traded futures lies with the clearinghouse after all transactions have been registered and the credit risk is
not with the original counterparties of the futures transaction. The greatest source of counterparty risk is brokers that are not members of a clearinghouse. Some financial institutions impose limits on the volume of
futures business that can be undertaken with brokers that are not mem-
Credit Risk
bers of a clearinghouse. These limits reduce the risk by number and value
of outstanding transactions with any particular broker. But the overall exposure for a futures broker is not as great as for the client, as the broker can
call for margin from the customer in order to mitigate the credit risk.
Before the counterparties enter into contracts with one another, they
usually agree on standard terms and conditions, to which both parties
agree. They also agree to rules on how disputes are to be settled. Exposure to Market Risks
Market risks have a substantial influence on valuation and on risk exposure.
Input variables such as the volatility of the underlying instrument, interest
rates, and equity price are required for the valuation of options. Any change
in these variables directly influences the valuation and thus exposes these
products to market risks with a higher leverage than the underlying instrument, as the option represents the right to sell or buy the principal amount
of the underlying instrument for the price of the option, which is substantially less. The clearinghouse is not directly affected by market risk factors,
as it passes the proceeds from the daily marking to market as an intermediary directly from one margin account to another, and thus carries no market
risk. The customer carries the market risk in the form of the margin account.
The customer can close out a contract by entering into a reverse transaction,
thus limiting losses to the amount in the margin account.
3.11.5 Options
In general, an option gives to the buyer the right, but not the obligation, to
buy or sell a good at a specific quantity at a specific price (strike price) on
or before a specific date in the future (maturity date). Many different types
of option contracts exist in the financial world. The two major types of
contracts traded on organized options exchanges are calls and puts. The
contracts are available for a wide variety of underlying instruments:
Interest-rate-sensitive products
Other derivatives, such as futures, and so forth
Some options trade on over-the-counter (OTC) markets. The OTC
market offers an advantage in that that the terms of the option contract
(exercise price, maturity date, committed underlying instrument) can be
tailored to the needs of the traders or clients. Option contracts traded on
an exchange are for defined underlying instruments with standardized
242 Description
The option-pricing approach is a valuation technique that relies on estimating the value of the embedded option. Option premiums fluctuate so
rapidly, as a function of price movements in the underlying instruments,
that computerized models are necessary to properly value them. The most
famous valuation model was developed by Black and Scholes; it is currently the foundation of models developed and used worldwide. Although the models are complex, their logic can be understood intuitively.
The intrinsic value is the value of an option that is immediately exercised.
A rational investor would never exercise a call when the underlying asset
price is below the exercise price. When the option is not worth exercising,
it is out of the money or at the money. The intrinsic value cannot be negative,
as the buyer of a call has the right but not the obligation to exercise. The
option has a time value, even if the intrinsic value is zero. The time value
reflects the probability that the option will move into the money and
therefore acquire an intrinsic value. The time value is an increasing function of the time to expiration. The likelihood of this happening decreases
as the option’s remaining time to maturity decreases. The influence of
each of the input variables on a call option can be described as follows:
Exercise price. The higher the exercise price, the lower the
premium for the option on the same asset that has an identical
expiration date.
Interest rate. Options reduce the opportunity or financing cost
for claiming an asset. Thus, as interest rates rise, this
characteristic becomes more valuable, thereby raising the price of
the option—or, in a sense, the present value of the asset to be
purchased at expiration is reduced.
Volatility. The more volatile the asset, the larger the expected
gain on the option; hence, the larger its premium.
Time to expiration. The value of an option is an increasing
function of the time to expiration. The leveraging advantage
mentioned earlier increases with time. The opportunity for the
underlying instrument price to exceed the exercise price increases
over time. Time compounds both the interest rate and volatility
All determinants of the option premium, except the underlying asset
volatility, can be measured precisely. The underlying asset volatility is
usually estimated with the implicit volatility.
Options can be used for different purposes:
Hedging. Buying an option can be used to hedge the underlying
position. Options are potentially attractive, as they serve as
hedges to equalize adverse movement in prices. Written options
Credit Risk
can also be used for hedging, particularly when the writer has the
underlying position (covered call).
Arbitrage trading. Options can be traded by buying and selling
options that appear to be over- or underpriced compared to
similar products issued by different counterparties, using
different valuation models, to generate an arbitrage position.
Asset–option and option–option trading. Options can be traded by
buying and selling options to combine these options with each
other or in combination with underlying instruments to produce
structured products with risk–reward profiles different from
those of the underlying instrument or the individual option.
Speculation. Speculation can be regarded as a special case of
trading with open option positions. The speculator expects that
the actual future movements of the underlying instrument or the
individual option will differ from the expected movements
(expected parameters) inherent in the current option price. The
speculators take direct open positions (i.e., selling a call without
the underlying instrument and expecting the instrument price to
decrease) or with structured combinations of options (i.e., selling
a strangle). Inherent Risk Types
Credit risk is limited to the valuation of an option and does not include the
overall amount of the underlying instruments. A traded option purchased
at the exchange has a credit risk limited to the price paid to the broker or the
exchange. A written option (short selling) has a credit risk limited to the option premium to be received. But as written options are settled long before
the option is exercised, the credit risk from the settlement of the premium
rarely arises. The credit risk exposure from exchange-traded options is considered to be less than the exposure from OTC options, because settlement
procedures and standardized parameters support efficiency in settlement.
Market risks have an important influence on the overall risk exposure of options, as most of the input variables (currencies, interest rates,
equity prices, volatility coefficient, etc.) are market risk factors. Quantification of Credit Risks
The quantification of credit risks from options can be treated similarly to
that from other off-balance-sheet exposures. The bank’s credit risk on a
purchased exchange-traded option is limited to the price of the option and
not to the overall value of the contract (principal value of the underlying
instruments). The credit exposure can be measured by the margin deposits placed with brokers or exchanges. The credit exposure of short calls
is limited to the price due from the counterparty. The credit risk exposure
from exchange-traded options is considered to be less (almost risk free)
than the exposure from OTC options purchased directly from counterparties, because settlement procedures and standardized parameters support
efficiency in settlement.
Credit risk exposure is generally captured on a counterparty basis.
Banks usually apply two methods for the quantification of credit
Some banks apply a percentage on the principal amount of the
underlying instruments to estimate a credit equivalent for these
exposures. This method does not take into account the current
market exposure of the option reflecting the changes in the input
variables; and
Most banks calculate the credit risk equivalent using the actual
market value of the option plus a safety margin for likely future
changes over the remaining time to expiration of the option. The
two most important input variables for the option valuation
market price and volatility are modified by adding a safety
margin. The quantification of credit risk would be the revaluated
option price based on the modified input parameters. This
approach corresponds to scenario-analysis as required by
different regulations (or regulators). Exposure to Market Risks
Market risks have a substantial influence on valuation and on risk exposure. Input variables such as the volatility of the underlying instrument,
interest rates, and equity price are required for the valuation of options.
Any change in these variables directly influences the valuation and thus
exposes these products to market risks with a higher leverage than the underlying instrument, as the option represents the right to sell or buy the
principal amount of the underlying instrument for the price of the option,
which is substantially less.
3.11.6 Forward Rate Agreements Description
Forward rate agreements (FRAs) are private contracts between two parties (usually written by banks), which guarantee a client the borrowing or
lending interest rate at a future time. On the expiration date of the FRA,
the bank pays or receives the difference between the agreed interest rate
and the interest rate prevailing in the marketplace at the time. An FRA is a
contract for difference—the amount settled is the difference between the
market interest rate at the settlement date and the interest rate fixed in the
FRA contract. The FRA is disconnected from the actual lending or bor-
Credit Risk
rowing. The bank simply pays or receives the interest-rate difference at
maturity but does not lend to or borrow from the client.
The effect of an FRA is to lock a fixed interest rate as an expense to
one counterparty and as income to the other. No payment is required if
market rates on the settlement date equal the forward rates as fixed on the
contract date. To the extent that market rates diverge from the forward
rate, one party has to compensate the other for the difference. The notional
amount (principal) does not change hands. Forwards are like tailor-made
futures to suit an investor’s exact requirements, but they are mainly OTC
products rather than exchange traded.
Forward rate agreements can be used for different purposes:
As FRAs can be tailored to the client’s needs, they can be used as
hedges. An investor who expects a large amount at a specific date
in the future, and a significant reduction in interest rates in the
near future, may enter into a forward rate agreement to receive a
fixed rate of interest in the future, which will become increasingly
profitable to the extent that the interest rate decreases as
expected. The investor is compensated by the profit from the FRA
for the lower interest rate at which the expected amount can be
invested in the future.
FRAs can be used as trading instruments. A financial institution
which expects a significant decrease in interest rates may engage
in a FRA by receiving a fixed rate of interest, which will increase
in value to the extent that the expected reduction in the market
rate actually occurs. Inherent Risk Types
The FRA is exposed to market and credit risks. Quantification of Credit Risks
The term credit risk means an investor’s exposure to a counterparty unable to
fulfill obligations. The credit risk on an FRAis limited to the amount of the settlement payment and not the notional amount plus interest. The credit risk is
calculated as the replacement value of the FRA (i.e., the current market value
of the FRA). The replacement value is defined as the movement in interest rates
since the contract date. Depending on the direction (up or down) of market
interest rates relative to the contractual interest rates, an actual loss or profit
can be generated. Credit risk must therefore be calculated in relation to future
interest-rate volatility (i.e., implicit volatility), which can only be estimated.
Using historical interest-rate fluctuations and option-pricing models (incorporating parameters such as time to maturity and the particular interest rate
subject to the FRA contract), it is possible to calculate a range for the implicit
volatility, within which interest-rate movements are expected to remain.
246 Exposure to Market Risks
As FRAs are based on interest rates, market risks have a substantial influence on the valuation and the risk exposure. For the time period between
the settlement date and maturity, interest rates are locked in. After this
time period, the amount is again exposed to movements in interest rates.
3.11.7 Asset-Backed Securities Description
Asset-backed securities (ABSs) are a relatively new category of marketable securities that are collateralized by financial assets like accounts
receivable (most commonly), mortgages, leases, or installment loan contracts. Asset-backed financing involves a process called securitization. Securitization is a disintermediation process in which the credit from
commercial or investment banks and other lenders is replaced by marketable debt securities that can be issued at a lower cost. Securitization involves the formation of a pool of financial assets so that debt securities can
be sold to external investors to finance the pool.
Securitization generates structured and complex instruments, which
are not easy to price. But investors continue to demand all kinds of exotic
forms of securities. Creative security design often calls for bundling basic
and derivatives securities into one composite security. A convertible is a
bundled security of preferred stock with options. Quite often, the creation
of an attractive security requires the unbundling of an asset for pricing on
the investor side. For example, a mortgage pass-through security is unbundled into two classes. Class 1 receives only principal payments from
the mortgage pool, whereas Class 2 receives only interest payments. Other
financial instruments have to be unbundled in a similar manner to assess
an appropriate price.
Asset-backed securities can take the following forms:
Repurchase agreements (repos). These are money market securities
that date back to the 1950s. Repos are the oldest asset-backed
security. (See the discussion of repo instruments in Section 3.11.3.)
Mortgage-backed securities. A security is either an ownership
claim in a pool of mortgages or an obligation that is secured by
such a pool. These claims represent the securitization of mortgage
loans. Mortgage lenders originate loans and then sell packages of
these loans in the secondary market. The claims are sold for the
cash inflows from the mortgages as those loans are paid off. The
mortgage originator continues to service the loan, collecting
principal and interest payments, and passes the payments along
to the purchaser of the mortgage. Mortgage pass-through securities
(MPTSs) are certificates backed by a pool of insured mortgages.
Credit Risk
They were first sold in 1970 by the Government National
Mortgage Association (GNMA), called Ginnie Mae. MPTs are
popular in spite of their prepayment uncertainty because MPTS
issuers get to remove the mortgage assets and all associated
liabilities from their balance sheets. Mortgage-backed bonds (MBBs)
are debt securities that have their credit enhanced by being
overcollateralized and by the purchase of credit insurance. In
overcollateralization, the MBB issuer takes a residual risk
position in the pool.
Collateralized mortgage obligations (CMOs). Issued by the Federal
Home Loan Mortgage Corporation (FHLMC), called Freddie Mac,
these are multiclass debt securities used to finance a pool of
insured mortgages. CMO investors own bonds that are
collateralized by a pool of mortgages or by a portfolio of
mortgage-backed securities. The bonds are serviced with the cash
flows from these mortgages; however, rather than using the
straight pass-through arrangement, the CMO substitutes a
sequential distribution process that creates a series of bonds with
varying maturities to appeal to a wider range of investors.149 The
disadvantages of CMOs are that the issuer must retain the lowest
class of CMO until the entire pool is liquidated, and the issuer
must show the pool’s assets and liabilities on its balance sheet.
Student loans. First pooled and sold in 1973 by the Student Loan
Marketing Association (SLMA), called Sallie Mae. The SLMA
sponsors pass-throughs backed by loans originated under the
Guaranteed Student Loan Program and by other loans granted
under various U.S. federal programs for higher education.
These securities were supported by U.S. federal government agencies that insure the pools of financial assets against default. The profitability and liquidity of these government-subsidized financing plans set the
stage for the private securitization programs, such as the following:
Trade-credit-receivable-backed bonds. These are pools of tradecredit receivables, first issued by American Express in 1982.
Certificates amortizing revolving debts (CARDs). These are pools of
credit card receivables, first issued by Salomon Brothers in 1986.
Securitization usually involves the creation of new debt securities.
As a result, the default risk, traditionally borne by equity investors, must
be assumed by some other method. Credit enhancement is typically accomplished via the following procedures:
The assets to be financed are placed in a trust as collateral with a
third party, usually a depository bank.
The next step is to provide for AAA- or at least AA-grade rating
for the collateral from major credit-rating agencies such as
Moody’s or Standard & Poor’s. If the proper credit enhancement
arrangements can not be made, investors’ risk aversion will keep
them from buying the new debtlike securities. Several methods of
obtaining a high credit rating for securitized assets exist, such as
guarantees, overcollateralization, purchase of insurance from an
insurance company, and diversification by geography or industry.
Typical benefits obtained from securitization are as follows:
Funds flow more efficiently from investors to borrowers as the
bundled financial assets gain liquidity. Assets may be illiquid
individually (such as mortgages), but when repackaged and
securitized they become liquid financial securities. Liquidity is
one of the primary goals of securitization.
Prepayment risks borne by the seller of the financial assets are
transferred to the investor.
Diversification opportunities are increased for the seller and the
The seller of the financial assets can avoid the interest rate risk
and default risk associated with carrying assets in the books.
Lower-cost financing for inventories of financial assets may be
available. Inherent Risk Types
As with all credit, the primary risk is that the borrowers will default and
be unable to repay the principal and the interest outstanding. Thus, the
rating and the corresponding term structure of interest rates (quality
spread) reflect the credit risk.
As ABSs are based on interest rates, market risks have a substantial
influence on the valuation and the risk exposure. Quantification of Credit Risks
Credit risk exposure can be measured by the rating difference of the collateralized assets before and after the credit enhancement, which results in
a quality spread in favor of the new debt securities. This risk is carried by
the trust, which involves the collateralized assets on one side of the balance sheet and the equity capital, in the form of the securities, on the other
side. The bank usually carries only the counterparty risk for the transaction if ABSs are bought from or sold to investors. Exposure to Market Risks
As ABSs are based on interest rates, market risks have a substantial influence on the valuation and the risk exposure.
Credit Risk
Most asset-backed securities are liquid, because the investment
banking firm that securitizes the assets agrees to maintain a liquid secondary market in the securities.
3.11.8 Interest-Rate Swaps Description
While there are numerous types of interest-rate swaps (IRSs), the most
common is the plain-vanilla or generic swap that involves two parties
(called counterparties) swapping fixed payments for floating-rate payments. For example, assume that one party has issued a floating-rate security that makes payments determined by a floating index. Floating-rate
liabilities are risky because the borrower bears the risk of rising interest
rates, which could prove unfortunate. It is possible that the firm or government that has issued a floating-rate security might prefer to make
fixed-rate payments, while other parties in the market might have the opposite position, wherein they are required to make fixed payments but
would prefer floating-rate payments. This might be the case if the party
held assets that had floating-rate coupons. If it had floating-rate liabilities
and floating-rate assets, the interest rate payments it makes would tend to
move up and down with the interest-rate payments it receives. Changes in
the level or structure of the term structure of interest rates would not affect
the overall difference of interest rates to be paid and received.
The interest-rate benchmarks that are commonly used for the floating
rate in an interest rate swap are those on various money market instruments: Treasury bills, the London interbank offered rate (LIBOR), commercial paper, banker’s acceptances, certificates of deposit, and the prime rate.
Market participants can use an interest-rate swap to alter the cashflow character of assets or liabilities from a fixed-rate basis to a floatingrate basis, or vice versa. The only cash flows that are exchanged between
the parties are the interest payments, not the notional principal amount.
In most cases, an intermediary is needed, which is the function of the
swap dealer, a firm that arranges swaps between other firms. In order to
understand the swap activity, it is important to determine the various
roles of the bank in this process. The different roles determine the risk exposures and the required control procedures as well as the accounting
treatment. The bank can enter into a swap transaction for three reasons:
For trading purposes
As an intermediary
For hedging purposes
A bank may act as trader and use swap transactions for trading or
speculative purposes. Having a view on the future development of interest rates (or currency), the bank would not seek to enter an offsetting swap
but would be exposed by a one-sided deal, depending on its view. For ex-
ample, a bank expecting interest rates to decrease might enter into a swap
paying a floating rate and receiving a fixed rate. This strategy is similar to
lending in the money market for a contractual term at a fixed rate and borrowing the proceeds for shorter periods at variables rates.
Acting as an intermediary, the bank will arrange and administer the
swap transaction. A counterparty seeking a swap will approach the bank,
which will identify another counterparty with opposite interest-rate requirements. In most cases, the counterparties are unaware of each other,
and the bank will exchange the interest payments and take a spread on the
interest rate as compensation for its role as intermediary. The bank can act
as principal or as an agent. If the bank acts as principal, the counterparties
enter into a contract with the bank, and both parties rely on the bank,
rather than on each other, for performance under the deal. Should one
party default, the bank as principal is still obligated to the other party. The
bank as intermediary substitutes its credit for the credit of the two counterparties, and in doing so, accepts the credit risks from both counterparties. The bank’s exposure is not the full (notional) amount but is limited to
the interest-rate cash flow to be paid by the defaulting party.
Using swap transactions to hedge existing or future transactions
(with a forward swap) of assets and liabilities, the bank is exposed, for example, to the offset of variable-rate assets and fixed-rate liabilities. A decrease in interest rates would have a significant impact on hedged
positions and profitability. In this example, the bank has two alternatives:
it might enter a swap and convert the variable-rate assets into fixed-rate
assets, or convert the fixed-rate liabilities into variable-rate obligations. In
both cases the bank has the assurance that the overall earnings situation
remains stable regardless of the direction in which interest rates move.
Smaller banks and individual portfolio managers tend to manage
their portfolios on a deal-by-deal basis. Larger banks use portfolio hedging, in which all cash flows from all swap deals are aggregated. Because
not all deals can be perfectly matched (in terms of principal, reset dates,
etc.), the remaining exposure has to be hedged or not, based on known future cash flows or by reducing exposures that have different swap reset
dates or maturity dates. Inherent Risk Types
A swap is exposed to market, credit, and operational risks. The operational risk is primarily a settlement risk. Counterparty risk is part of the
credit risk and is the main credit exposure. Like other off-balance-sheet instruments, the amount at risk is the cash flows (interest rates) to be exchanged and not the notional amount. Therefore, exposure is measured
after determining an appropriate credit equivalent amount.
The amount at risk is exposed and is a function of the following
Credit Risk
Counterparty risk. This presents the biggest part of the risk
Operational risk. In particular, settlement risks.
Type of swap contract. Swaps are generally riskier for a fixed maturity
due to the added risk of exchange- or interest-rate movements.
Term to maturity of swap contract. The longer the term to
maturity, the more cash flows are outstanding and are exposed to
interest-rate and currency movements over longer time horizons.
Payment mismatch. Especially in a swap portfolio, swaps result
in one party making payments prior to receiving payments—for
example, one party makes semiannual payments (fixed rate) but
receives quarterly payments (floating rate). Quantification of Credit Risks
The quantification of credit risk is a function of the net present value of the
swap and the counterparty ratings. Bank accountants and swap dealers
use the net present value approach to determine the value of the swap.
The replacement costs in terms of interest and currency rates for the fixed
and variable cash flows are used to measure the present value. A swap,
under which the bank receives 6 percent and pays LIBOR, where the replacement cost of the fixed leg is currently 4.5 percent, results in a profit
upon valuation equal to the monetary effect of the 1.5 percent fixed-interest-rate differential over the term of the swap (with future cash flows discounted). If the bank paid 5.5 percent on the fixed leg (instead of the
current market rate of 4.5 percent) this would result in a loss upon valuation of 1 percent discounted over the term of the swap. The matched
transactions leave the bank a profit of 0.5 percent per annum on the national amount of the swap (the bank is receiving 6 percent and paying 5.5
percent on the offsetting legs of the two swaps). The NPV for a matchedswap deal will therefore generally be equal to the current value of the
bank’s spread on the cash flows being exchanged over the life of the deal.
This amount at risk can be used for the determination of the counterparty risk. Exposure to Market Risks
The amount of interest-rate payments exchanged is based on the predetermined principal, which is called the notional principal amount. But as the
counterparties agree to exchange periodic interest payments, the notional
amount is not transferred. The swap position can be regarded as a series of
forward or futures contracts, or a series of cash flows resulting from buying
and selling cash market instruments. In both cases, the cash flows are exposed to interest- and currency-rate movements over the time horizon. Table
3-19 shows the risk–return profile in the case of interest-rate movements.
T A B L E 3-19
Risk–Return Profile for Counterparties to an Interest-Rate Swap
Interest-rate movement
Floating-rate payer
Fixed-rate payer
The long futures positions gain if interest rates decline and lose if interest rates rise. This is similar to the risk–return profile for a floating-rate
payer. The risk–return profile for a fixed-rate payer is similar to that of the
short futures position: a gain if interest rates increase and a loss if interest
rates decrease.
A portfolio approach to credit risk management is the most important alternative approach to the current standardized capital rules. Portfolio
credit risk modeling shares the advantages of portfolio market risk modeling, which have already been recognized by the leading regulatory bodies. These include:
Ability to take an integrated view of credit risk across a financial
institution. This makes possible the comparison of the relative
risk of a 1-year $10-million loan, a 10-year $1-million bond, and a
10-year partly collateralized swap with a $10-million positive
mark-to-market value.
Ability to assess concentration and diversification. By taking a
portfolio approach, a credit risk model recognizes the risks of
concentrated exposures (to a single counterparty or to a group of
highly correlated counterparties) and the benefits of
Ability to take a dynamic view of credit risk. In contrast to the
fixed standard capital rules, the model approach is based on
actual default and recovery rates.
There has been dynamic development in the markets in recent years,
which must be reflected in the regulations in order to support manage-
Credit Risk
ment dynamically in a business sense, instead of relying on the fixed standard capital rules:
Lenders should focus on risk-adjusted performance
Risk-adjusted capital allocation across different business activities
is needed.
Risk transfer by means of securitization is needed.
Institute of International Finance
In a 1998 discussion paper, the Institute of International Finance (IIF)
proposed abandoning the rigid and inflexible system of 100 percent capital requirements for the private sector and introducing a more differentiated system for risk assessment, based on the credit quality of the
The IIF also suggested introducing complex credit models, which
could be developed and enhanced depending on the complexity of the instruments and the quality of the models used for modeling the risks. Similar to the model-based approach, the incentive for the implementation of
complex credit risk management systems is risk-adequate valuation resulting in lower capital requirements for those risks.
The IIF uses the following premises, whereas the BIS, as the regulatory body, has to define the terms and assumptions in detail:
Capital adequacy requirements based on the probability
distribution of credit loss of the credit portfolio
Consistent methodology for all counterparty ratings for all credit
Estimates of probability distribution regarding potential losses of
the credit portfolios
Estimates of correlations between the probability distributions of
credit positions within a credit portfolio
Estimates of the expected credit losses based on the ratings and
the related statistical loss distributions as well as the loss severity
in the case of credit defaults
Estimates of the unexpected credit losses for the entire portfolio
(e.g., with the VaR approach)
Description of the data sources and documentation of the model
approach assumptions
Stress-testing procedures to quantify extreme credit losses over
the statistical confidence levels
3.12.2 International Swaps
and Derivatives Association
The International Swaps and Derivatives Association (ISDA) proposed a
three-stage approach, which, like the IIF approach, is based on the incentive that a risk-adequate approach is directly related to lower capital
The first stage is the current practice, with the possibility of offsetting
risks by hedging positions in credit derivatives. The second stage is similar
to the standard approach for supporting market risk; it is a simplified
model that considers the counterparty rating and the term to maturity of
the credit risk positions, and it includes several offsetting and netting possibilities. The third stage considers credit portfolio risk models. These models consider the correlations between credit positions and thus allow the
use of the diversification effect of a risk-adequate, but complex and expensive, approach to the capital adequacy calculation for credit risks. This
approach requires an enormous amount of input data, such as loss probability distributions, recovery rates, and credit spreads.
The discussion papers of the IIF and the ISDA are valuable contributions to the discussion of the next generation of credit risk regulations. The
proposal of the ISDA to maintain the existing regulations in a slightly extended version could be misunderstood in view of the existing problems
and weaknesses of the current regulations. A standardized approach that
could be used by all institutions and would reflect the credit risk in a more
accurate way would lead to more adequate capital requirements. This
would be the basis for a concept similar to the capital accord supporting
market risks, which requires that the lead regulators be able to approve internally used models (partially in use already). As in the market risk regulations, stringent quantitative and qualitative assumptions would have to
be fulfilled before regulators could grant approval. Stress tests would be
critical in reviewing the model quality, as backtesting is difficult with
credit models.
Basel Committee on Banking Supervision
and the New Capital Accord
The original accord focused mainly on credit risk. It has since been
amended to address market risk. Interest-rate risk in the banking book
and other risks, such as operational, liquidity, legal, and reputational
risks, are not explicitly addressed. Implicitly, however, the present regulations take such risks into account by setting a minimum ratio that has an
acknowledged buffer to cover unquantified risks.
The current risk weighting of assets results, at best, in a crude measure of economic risk, primarily because degrees of credit risk exposure are
Credit Risk
not sufficiently calibrated as to adequately differentiate between borrowers’ differing default risks.
Another related and increasing problem with the existing accord is
the ability of banks to arbitrage their regulatory capital requirement and
exploit divergences between true economic risk and risk measured under
the accord. Regulatory capital arbitrage can occur in several ways—for example, through some forms of securitization—and this can lead to a shift
in banks’ portfolio concentrations to lower-quality assets.
In 1999, the Basel Committee on Banking Supervision decided to introduce a new capital adequacy framework152 to replace the initial accord
from 1988.153 The new accord is designed to improve the way regulatory
capital requirements reflect underlying risks. This new capital framework
consists of three pillars:
Minimum capital requirements
A supervisory review process
Effective use of market discipline
With regard to minimum regulatory capital requirements, the BIS is
building on the foundation of the current regulations, which will serve as
a standardized approach for capital requirements at the majority of banks.
In doing so, the paper proposes to clarify and broaden the scope of application of the current accord. With regard to risk weights to be applied to
exposures to sovereigns, the BIS proposes replacing the existing rigid approach with a system that allows using external credit assessments for determining risk weights. It is intended that such an approach will also
apply (either directly or indirectly and to varying degrees) to the risk
weighting of exposures to banks, securities firms, and corporations. The
result will be to reduce risk weights for high-quality corporate credits, and
to introduce a risk weight higher than 100 percent for certain low-quality
exposures. A new risk-weighting scheme to address asset securitization
and the application of a 20 percent credit conversion factor for certain
types of short-term commitments are also proposed.
For some sophisticated banks, the BIS believes that an internal ratings-based approach could form the basis for setting capital charges, subject to supervisory approval and adherence to quantitative and qualitative
guidelines. The BIS believes that this will be an important step in the effort
to align capital charges and underlying risk more closely.
The BIS wants to incorporate the model approach (similar to the capital adequacy regulation supporting market risks) in the credit portfolio
risk modeling to be used for regulatory capital calculation.
At some of the more sophisticated banks that make use of internal
ratings, credit risk models based on these ratings (and other factors) have
also been developed. Such models are designed to capture the risk from
the portfolio as a whole—an important element not found in approaches
based solely on external credit assessments or internal ratings. The BIS
supports the fact that these models are already in use in some banks’ risk
management systems, and it recognizes their use by some supervisors in
their appraisals. However, the paper recognizes that due to a number of
difficulties, including data availability and model validation, credit risk
models are not yet at the stage where they can play an explicit part in setting regulatory capital requirements. The BIS will verify how this could
become possible after further development and testing, and it intends to
monitor progress on these issues closely.154
The recent development of credit risk mitigation techniques such as
credit derivatives has also enabled banks to substantially improve their
risk management systems. The current accord does not incorporate the
development of specific forms of credit risk mitigation by placing restrictions on both the types of hedges acceptable for achieving capital reduction and the amount of capital relief. The current solution leaves open the
treatment of imperfect credit risk protection (such as maturity mismatches, asset mismatches, or potential future exposure on hedges), resulting in the development of different national policies. The new accord
committee proposes a more consistent and economic approach to credit
risk mitigation techniques, covering credit derivatives, collateral, guarantees, and on-balance-sheet netting (see Annex 2 of the new capital accord).
The BIS recognizes that maturity of a claim is a factor in determining
the overall credit risk it presents to the bank. The paper is somewhat unclear on this point, as it clearly says that the paper at present is not proposing to take maturity of claims into account for capital adequacy
purposes, except in a very limited case. Nonetheless, it claims as well to
distinguish more precisely among the credit quality of exposures, and it
also will consider ways to factor maturity more explicitly into the assessment of credit risk.155
The BIS will also consider what changes may be needed to the market
risk component of the regulations to enhance consistency of treatment between the banking and the trading books and to ensure adequate capital
coverage for trading-book items, and it will consider ways to follow up on
recommendations contained in earlier documents. For credit risk, the
paper states that the objective of a more comprehensive treatment of risk,
with capital charges that are more sensitive to risk, can be met in varying
ways depending on the time frame under consideration (time to maturity)
and on the technical abilities of banks and supervisors (models). The paper
proposes three approaches for setting minimum capital requirements:
A modified version of the existing approach
The use of banks’ internal ratings
The use of portfolio credit risk models
Credit Risk
The existing regulations specify explicit capital charges only for
credit and market risks in the trading book (Figure 3-32). Other risks, including interest-rate risk in the banking book and operational risk, are
also an important feature of banking. The committee therefore proposes to
develop a capital charge for interest-rate risk in the banking book for
banks whose interest-rate risk is significantly above average. The committee also proposes to develop capital charges for other risks, principally
operational risk.156
The new operational risk regulations include the results of an informal survey that highlight the growing realization of the significance of
risks other than credit and market risks, such as operational risk, which
have been at the heart of some important banking problems in recent
years. A capital charge based on a measure of business activities (such as
revenues, costs, total assets, or, at a later stage, internal measurement systems) or a differentiated charge for businesses with high operational risk,
based on measures commonly used to value those business lines, is calculated to support operational risks. Particular regard will need to be paid to
the potential for capital arbitrage, to any disincentives to better risk control that might thereby be created, and to the capital impact for particular
F I G U R E 3-32
New Structure of Capital Requirements, Broken Down by Risk Categories.
Market risks
Market risks
Credit risks
Credit risks
types of banks. Qualitative factors such as the integrity of the controls
process and internal measures of operational risk should be considered.
The BIS has recognized the significance of interest-rate risk within
some banking books, depending on a bank’s risk profile and market conditions. Accordingly, the BIS proposes to develop a capital charge for interest-rate risk in the banking book for banks whose interest-rate risks are
significantly above average (outliers). The BIS recognizes that some national discretion would be necessary regarding the definition of outliers
and the methodology used to calculate interest-rate risk in the banking
book. At the same time, the BIS intends to examine developments in
methodologies as set out in its 1993 paper on the measurement of exposure to interest-rate risk to identify those banks which are outliers.157 The
BIS will consider alternative methodologies for capital charges, including
allowing for national discretion and basing such charges on internal measurement systems that are subject to supervisory review, and it will seek
comments from the industry.
For the measurement of credit risk, two principal options are being
proposed in the new accord. The first is the standardized approach; the
second is the internal ratings-based (IRB) approach. There are two variants of the IRB approach, foundation and advanced. Use of the IRB approach will be subject to approval by the supervisory body, based on the
standards established by the committee. Standardized Approach
for Measuring Credit Risk
The standardized approach is conceptually the same as the present accord,
but is more risk sensitive.158 The bank allocates a risk weight to each of its assets and off-balance-sheet positions and produces a sum of risk-weighted
asset values. A risk weight of 100 percent means that an exposure is included
in the calculation of risk-weighted assets at its full value, which translates into
a capital charge equal to 8 percent of that value. Similarly, a risk weight of 20
percent results in a capital charge of 1.6 percent (i.e., one-fifth of 8 percent).
Individual risk weights currently depend on the broad category of
borrower (i.e., sovereign, bank, or corporate). Under the new accord, the
risk weights are to be refined by reference to a rating provided by an external credit assessment institution (such as a rating agency) that meets
strict standards. For example, for corporate lending, the existing accord
provides only one risk-weight category of 100 percent, but the new accord
will provide four categories (20, 50, 100, and 150 percent). IRB Approach for Measuring Credit Risk
Under the internal ratings-based (IRB) approach, banks will be allowed to
use their internal estimates of borrower creditworthiness to assess credit
risk in their portfolios, subject to strict methodological and disclosure stan-
Credit Risk
dards.159 Distinct analytical frameworks will be provided for different types
of loan exposures, such as corporate and retail lending, whose loss characteristics are different. Under the IRB approach, a bank estimates each borrower’s creditworthiness, and the results are translated into estimates of
potential future losses, which form the basis of minimum capital requirements. The framework allows for both a foundation method and more advanced methodologies for corporate, sovereign, and bank exposures. In the
foundation methodology, banks estimate the probability of default associated with each borrower, and the supervisory authority supplies the other
inputs. In the advanced approach, a bank with a sufficiently developed internal capital allocation process will be allowed to supply other necessary
inputs as well. Under both the foundation and advanced IRB approaches,
the range of risk weights will be far more diverse than those in the standardized approach, resulting in greater risk sensitivity.
Banks will be required to categorize banking-book exposures into six
broad classes of assets, as shown in Figure 3-33. The internal rating systems must meet the following criteria:
Must have been in use at least three years (except equity and
project finance categories)
Must be two-dimensional systems
Must incorporate minimum annual ratings reviewed by an
independent credit risk control unit
Must incorporate an effect process for updating and reflecting
changes in a borrower’s financial condition within 90 days; 30
days for borrowers with weak credit
F I G U R E 3-33
Banking Book Categories for Internal Ratings-Based Approach.
Regulatory guidelines
Project finance
Less developed
Well developed
Probability of Default
Under the foundation and advanced IRB approaches, the probability of
default (PD) defined by bank must comply with the following regulatory
Must be consistent with the regulatory definition of default
Must use a one-year time horizon
Must be forward looking
Must have a minimum default probability of 3 basis points
Must be based on at least five years of data
Must collect internal data and consider mapping to external data
and statistical default models
May use pooled data, but must demonstrate that the internal
rating systems and criteria of other banks are comparable to own
Retail Exposures
The calculation of retail exposures is similar in most respects to that for
corporate exposures, with some important exceptions. The bank is expected to segment its retail exposures on the basis of the following four
Product type
Borrower risk (e.g., credit score)
Delinquency status (minimum of two categories for borrowers in
Vintage (maximum one-year buckets).
Additional segmentation techniques may be employed (e.g., borrower
type and demographics, loan size, maturity, loan to value).
There are two options for assessing the risk components:
Separately assess PD and loss given default (LGD)
Assess a single expected loss (PD × LGD).
The retail-exposure approach has no equivalent in the foundation
approach. Advanced IRB Approach
Only a small number of banks are expected to qualify due to rigorous eligibility requirements. The banks must agree to an aggressive rollout plan.
Once a financial organization opts for the advanced IRB approach for one
risk element, it must adopt its own estimates for other risk factors in a reasonably short period of time for all significant business units and exposure
classes. During this period there will be no capital relief granted for intra-
Credit Risk
group transactions between the IRB bank and a business unit that uses the
standardized approach for business lines and exposure classes (this restriction is intended to minimize “cherry picking”). For the first two years
after implementation of the advanced IRB approach, the financial organization must calculate foundation and advanced approaches in parallel.
During the first two years following the date of implementation, the
benefit of the advanced IRB approach is limited by a floor set equal to 90 percent of the capital requirements resulting from the foundation IRB approach.
The advanced IRB approach requires full compliance with all foundation requirements (internal ratings system and PDs).161 In addition, the
following requirements have to be met:
Loss given default (LGD) grades must provide meaningful
differentiation of loss rates.
LGD and exposure at default (EAD) must be supported by at
least seven years of historical data and preferably a full business
The financial organization must provide evidence that it has a
robust system for validating LGDs.
Analysis of realized versus projected LGDs must be conducted at
least annually.
An independent unit must conduct stress testing of processes for
evaluating estimates of PD, LGD, and EAD on at least a sixmonth basis.
The Basel Committee is considering maturity as an explicit risk
driver, particularly with regard to the treatment of maturity
mismatches resulting from the use of certain credit risk
mitigation techniques and instruments.
All material aspects of the rating, PD, EAD, and LGD estimation
process should be approved by the board of directors,
management committee, and senior management.
Internal audits must include an annual review of the internal
ratings system.
Internal ratings should be incorporated into the internal
management reporting process.
Management must ensure that the rating process, criteria, and
outcome are comprehensively documented.
Documentation of risk factor methodologies must:
Provide a detailed outline of the theory, assumptions, and
mathematical and empirical basis of the assignment of PD
estimates to grades or individual obligors, and list the data
sources used to estimate the model.
Establish a rigorous statistical process for validating the selection
of explanatory variables.
Indicate the circumstances under which the model does not work
effectively. Validation and Stress Testing
The Basel Committee emphasizes validation and stress testing through
regulatory requirements.162 Banks must have in place a robust system to
validate the accuracy and consistency of rating systems, processes, and internal estimates of risk factors. Historical data time frames used for assessing the degree of respective data correlation should be as long as
possible, and should ideally cover a complete business cycle. Banks must
have in place sound stress-testing processes for use in the assessment of
capital adequacy. Testing must include identification of future changes in
economic conditions, or possible events that could unfavorably impact a
bank’s default estimations and therefore its overall level of capital adequacy. Stress testing must be performed on at least a six-month basis. The
output of testing should be periodically reported to senior management. Collateral
The new accord contains many new components and definitions regarding collateral:
The new accord provides for a broader definition of collateral.
The new accord allows for recognition of cash, a defined range of
debt securities, certain equity securities, units in mutual funds,
and gold.
Simple and comprehensive approaches to creating collateral
transactions are proposed:
The simple approach generally uses the current substitution
The comprehensive approach focuses on the cash value of
collateral (conservative estimate).
Banks are required to account for changes in the value of their
exposures and in the value of collateral received.
Accounting is to be accomplished through the use of “haircuts”
to reflect exposure volatility, the volatility of the collateral
received, and any currency volatility.
Banks may choose to use either standard supervisory haircuts or
those based on their own estimates of collateral volatility, subject
to minimum requirements.
The floor is set at 0 for very low risk transactions and 0.15 for all
other collateralized transactions.
Credit Risk
263 Credit Risk Mitigation and Securitization
The new framework introduces more risk-sensitive approaches to the
treatment of collateral, guarantees, credit derivatives, netting, and securitization, under both the standardized approach and the IRB approach:163
The mitigation must be direct, explicit, irrevocable, and
The proposed “substitution ceiling” approach for guarantees and
credit derivatives is included under the advanced IRB
“Notching” is not permitted to extend beyond the higher of the
borrower or guarantor grades, thereby preventing any treatment
that is more favorable than full substitution.165
Guarantees and credit derivatives recognized as giving protection
receive a risk weight w of 0.15. Where the guarantor is a
sovereign, a central bank, or a bank, w will be 0.166
Guarantees that contain embedded options under which the
guarantor may or may not be obligated to perform will be
excluded from consideration. Asset Securitization
The committee is increasingly concerned by the employment of securitization structures by some banks with the intention of avoiding maintenance
of capital commensurate with their risk exposures.167 Specifically, an institution must comply with the definition of a “clean break,” and provide disclosure when the issuing bank removes securitized assets from its balance
sheet. The new accord contains severe penalties for implicit recourse:
Loss of favorable capital treatment for all assets associated with
the structure
Potential loss of favorable capital treatment for all securitized assets
The disclosure requirement of the new accord requires that banks
disclose qualitiative items and quantitative data in order to obtain capital
relief through the securitization process, as described in paragraphs 659
and 660 of the Pillar III section. These disclosures are required from banks
in their statutory accounts, whether they act as originators or sponsors or
third parties, and from issuers [special-purpose vehicles (SPVs)] in their
offering circulars.168 Granularity Adjustment to Capital
The granularity adjustment is an addition or subtraction to the baseline
level of risk-weighted assets described earlier in this document. IRB baseline risk weights are calibrated assuming a bank with exposures of “typi-
cal” granularity. The purpose of the granularity adjustment is to recognize
that a bank with exposures characterized by coarse granularity, implying
a large residual of undiversified idiosyncratic risk (i.e., single-borrower
risk concentrations), should require additional capital. Similarly, a bank
with exposures characterized by finer-than-average granularity should
demand a smaller-than-average capital requirement. Adjustments are incorporated into the IRB approach in the form of an addition or subtraction
to the baseline level of risk-weighted assets, and are applied across all
nonretail exposures under the IRB approach.169
To be incorporated by means of a standard supervisory capital adjustment, the bank has to take into account industry, geographic, or other
forms of credit risk concentration. There should be a meaningful distribution of exposure across grades, with no excessive concentrations in any
particular grade. Specifically, the committee is proposing that no more than
30 percent of the gross exposure should fall in any single borrower grade.
Based on the distribution of its exposures and LGD estimates within
(and across) its internal grades, a bank would calculate an adjustment to
risk-weighted assets to reflect the degree of granularity relative to a standard reference portfolio. Should a bank’s portfolio reflect a greater degree
of granularity than the reference portfolio, a reduction of risk-weighted
assets will be realized by the bank.
Conversely, upward adjustments to risk-weighted assets would be
required for bank portfolios reflecting lesser degrees of granularity than
the reference portfolio. Credit Derivatives
The treatment of credit risk mitigation techniques, and in particular credit
derivatives, is a contentious and highly technical area of the Basel Committee’s proposals. Banks involved in trading these instruments have expressed concern that, unless the proposals are amended, Basel’s plans
could stunt the growth of the young credit derivatives market. If banks get
preferential treatment for credit guarantees as opposed to credit derivatives, they may well be tempted to recharacterize derivatives as guarantees. This, too, could lead to market fragmentation and a rise in the cost of
credit to the market.
The committee believes that the most effective way forward would
be to treat this residual risk under the proposed framework’s second pillar (the supervisory review process), rather than by using the w factor
under the first pillar (minimum capital requirements) as proposed in the
original approach. The committee believes that this approach will allow
for a fairly simple, practical, and risk-sensitive framework for credit risk
management techniques.170
Another justification from Basel for the treatment of credit derivatives is the legal risk of these instruments. The market has adopted the 1999
Credit Risk
ISDA credit derivatives standard documentation. This has not proven foolproof, but it nonetheless represents a standardized agreement, as opposed
to the generally bilateral nature of traditional bank guarantees. Another
factor that may be worrying the regulators with regard to credit derivatives
is the double-default factor. This refers to the fact that in credit derivative negotiations, the trader intuitively considers the correlation between the
seller of protection and the underlying company it is selling protection
against (the reference entity). The Basel Committee has not justified this
omission by arguing that there is no correlation model that can explain it—
in other words, it does not have a reliable way of explaining and measuring the correlation. Some financial institutions suggest that a good
intermediate approach would be to divide the double-default issue into
transactions where there is a very high risk and those where the risk is low,
and set appropriate regulatory rules. Future developments, including an
empirical correlation based on models with adequate historical default correlation data, should not be excluded by Basel.
The treatment of credit derivatives on the trading book is another
important issue. If a bank sells protection on an entity in its trading book,
and at the same time it buys protection against the same entity for itself, it
would only obtain an 80 percent offset on regulatory capital. Some credit
derivatives traders fear that this could lead to distortions in pricing to absorb this extra capital charge, which in turn might distort credit risk models that are based on market spreads.
Credit risk has a long history; it evolved from an accounting foundation
into a discipline of its own. The perception of balance-sheet-based debts,
issued in many different forms (bonds, notes, subordinated, guaranteed,
etc.) has changed substantially over the past decades, through major
structural changes in the financial markets, such as the Brady bond crisis
and the Russian default of September 1998, causing major impacts in the
market and raising questions about the way credit risks are measured and
managed. Credit derivatives are one example of how credit risk has
evolved from a perceived loss area into a business line which generates
both profits and credit instruments that can be traded on a daily basis.
Over the past decade, a number of the world’s largest banks have developed sophisticated systems in an attempt to model the credit risk arising from important aspects of their business lines. Such models are
intended to aid financial institutions in quantifying, aggregating, and
managing risk across geographical and product lines. The outputs of these
models also play increasingly important roles in banks’ risk management
and performance measurement processes, including performance-based
compensation, customer profitability analysis, risk-based pricing and, to a
lesser (but growing) degree, active portfolio management and capital
structure decisions. Credit risk modeling has resulted in better internal
risk management, and will be used in the supervisory oversight of banking organizations. However, before a portfolio modeling approach is approved for use in the formal process of setting regulatory capital
requirements for credit risk, regulators want to be confident not only that
models are being used to actively manage risk, but also that they are conceptually sound, are empirically validated, and produce capital requirements that are comparable across institutions. At this time, significant
hurdles, principally concerning data availability and model validation,
have to be cleared before an organization is entitled to use a credit model
for calculating the capital requirements for credit risk. The new capital accord contains a new approach for looking at credit risk from a risk-sensitive standpoint, moving away from a formal and normative approach. It
allows the banks to choose from alternative approaches, depending on the
complexity of the credit portfolios, the credit instruments, and the capacity and complexity of credit risk management.
Models have already been incorporated into the determination of
capital requirements for market risk. However, credit risk models are not
a simple extension of their market risk counterparts for two key reasons:
Data limitations. Banks and researchers alike report that data
limitations are a key impediment to the design and
implementation of credit risk models. Most credit instruments are
not marked to market, and the predictive nature of a credit risk
model does not derive from a statistical projection of future prices
based on a comprehensive record of historical prices. The scarcity
of the data required to estimate credit risk models also stems
from the infrequent nature of default events and the longer time
horizons used in measuring credit risk. Hence, in specifying
model parameters, credit risk models require the use of
simplifying assumptions and proxy data. The relative size of the
banking book—and the potential repercussions on bank solvency
if modeled credit risk estimates are inaccurate—underscore the
need for a better understanding of a model’s sensitivity to
structural assumptions and parameter estimates.
Model validation. The validation of credit risk models is
fundamentally more difficult than the backtesting of market risk
models. Whereas market risk models typically employ a horizon
of a few days, credit risk models generally rely on a time frame of
one year or more. The longer holding period, coupled with the
higher confidence intervals used in credit risk models, presents
problems to model builders in assessing the accuracy of their
models. By the same token, a quantitative validation standard
Credit Risk
similar to that in the Market Risk Amendment would require an
impractical number of years of data, spanning multiple credit
This chapter analyzes the evolution of the credit risk models; the different approaches; the parameters, assumptions, and conditions which
characterize them; and their similarities to market risk models. Core sections of this chapter link the credit risk models and the new capital framework. Modern portfolio theory is well established in market risk and is in
the process of finding its way into credit risk. This chapter analyzes the
compatibility of market risk–driven parameters and assumptions in the
credit risk environment. A detailed section about the market risk component of credit risk instruments highlights the increasing overlap of the
market and credit risk areas.
3.14 NOTES
1. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Settlement Risk in Foreign Exchange Transactions: Report Prepared
by the Committee on Payment and Settlement Systems of the Central Banks of the
Group of Ten Countries, Basel, Switzerland: Bank for International Settlement,
March 1996.
2. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Sound Practices for Loan Accounting and Disclosure, Basel,
Switzerland: Bank for International Settlement, July 1999.
3. It is recognized that accounting guidance sometimes indicates that one or
the other of these two impairment tests (“it is probable that the bank will be
unable to collect” and “there is no longer reasonable assurance that the
bank will collect”) should be used. For instance, the probability test is
prescribed by IAS 39 and by the U.S. Financial Accounting Standards Board
(FASB) Statements of Financial Accounting Standards 5 and 114, while a test
of reasonable assurance is used in the Canadian Institute of Chartered
Accountants (CICA) Handbook Section 3025.03, and in guidance issued by
the British Bankers’ Association. An insignificant delay or insignificant
shortfall in amounts of payments does not necessarily constitute
impairment if, during such a period of delay, the lender can reasonably
expect to collect all amounts due.
4. The fifth amendment from the Basel Committee on Banking Supervision
was Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate Market Risks,
Basel, Switzerland: Bank for International Settlement, January 1996,
modified September 1997.
5. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, A New Capital Adequacy Framework: Consultative Paper by the
Basel Committee on Banking Supervision, Issued for Comment by 31 March 2000,
Basel, Switzerland: Bank for International Settlement, June 1999.
6. Christoph Rouvinez, “Mastering Delta Gamma,” Risk, (February 1997);
Mastering Delta Gamma, Zurich: Credit Suisse, 1999. For a detailed
discussion, see Gerold Studer, “Maximum Loss for Measurement of Market
Risk,” Ph.D. thesis, Swiss Federal Institute of Technology, Zurich, 1997.
7. For a detailed discussion, see P. Nickell, W. Perraudin, and S. Varotto,
“Stability of Rating Transitions,” paper presented at the Bank of England
Conference on Credit Risk Modeling and Regulatory Implications, London,
September 21–22, 1998. This study examines Moody’s ratings history over a
27-year period, indicating the influence of shifts in geographical and
industrial composition of the data set on published average transition
matrices, and it develops an ordered probit technique for deriving
transition matrices that are appropriate to the characteristics of the credit
exposures in the portfolio (e.g., industry and domicile of obligor, and stage
of business cycle).
8. Pamela Nickell, William Perraudin, and Simone Varotto, “Ratings versus
Equity-Based Credit Risk Modelling: An Empirical Analysis,” Working
Paper Series (132), Bank of England, London, 2001. This empirical study
implemented and evaluated representative examples of two of the main
types of credit risk models (ratings based and equity price based) and
assessed their performance on an out-of-sample basis using large portfolios
of eurobonds. Both models failed to provide an adequately large capital
buffer across the 10-year sample period; the portfolios experienced
“exceptions” at several times the rate predicted by VaR calculations based
on the models’ output.
9. For example, see J. A. Lopez and M. R. Saidenberg, “Evaluating Credit Risk
Models,” paper presented at the Bank of England Conference on Credit Risk
Modeling and Regulatory Implications, September 21–22 1998. It is reported
that a few survey participants relied on such alternative methods for
backtesting. These included: (1) comparing loan pricing implied by the model
with market pricing; (2) attempting to check the consistency of the main
drivers of modeling output (internal ratings and recovery rates) through
comparison with external benchmarks such as Moody’s and S&P; and (3)
backtesting on virtual portfolios, given the scarcity of data on credit events.
10. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Credit Risk Modelling: Current Practices and Applications, Basel,
Switzerland: Bank for International Settlement, April 1999, 13.
11. R. C. Merton, “On the Pricing of Corporate Debt: The Risk Structure of
Interest Rates,” Journal of Finance 29 (June 1974), 449–470.
12. Thomas C. Wilson, “Credit Portfolio Risk (I),” Risk (October 1997); “Credit
Portfolio Risk (II),” Risk (November 1997). McKinsey and Company,
CreditPortfolio View Approach Documentation and User’s Documentation,
Zurich: McKinsey and Company, 1998.
13. In practice each facility of a debtor is analyzed, to consider additional
features such as guarantees, options, etc. in the rating process. For
simplification, the assumption that ratings are associated with borrowers
is usually made.
Credit Risk
14. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Prudential Supervision of Banks’ Derivatives Activities, December
1994; Risk Management Guidelines for Derivatives, July 1994; Amendment to the
Capital Accord of July 1988, July 1994; Basel Capital Accord: The Treatment of the
Credit Risk Associated with Certain Off-Balance-Sheet Items, July 1994, Basel,
Switzerland: Bank for International Settlement.
15. Technology and the increased liquidity in the secondary market for loans
(along with the development of credit derivatives, though most are OTC)
have helped to move the lending paradigm away from a buy-and-hold
strategy to one in which credit risks are actively managed in a portfolio
framework. See A. Kuritzkes, “Transforming Portfolio Management,”
Banking Strategies (July/August 1998).
16. For a discussion, see J. A. Lopez and M. R. Saidenberg, “Evaluating Credit
Risk Models,” paper presented at the Bank of England Conference on Credit
Risk Modeling and Regulatory Implications, September 21–22, 1998; or Reto
R. Gallati, “De-Minimis-Regel diskriminiert,” Schweizer Bank 9 (Zurich,
1998), 41–43.
17. For a more complete discussion of these models, see J. B. Caouette, E. J.
Altman, and P. Narayanan, Managing Credit Risk: The Next Great Financial
Challenge, New York: John Wiley & Sons, 1998.
18. J. D. Taylor, “Cross-Industry Differences in Business Failure Rates:
Implications for Portfolio Management,” Commercial Lending Review
(January 1998), 36–46.
19. J. Stiglitz and A. Weiss, “Credit Rationing in Markets with Imperfect
Information,” American Economic Review (June 1981), 393–410.
20. W. Treacy and M. Carey, “Internal Credit Risk Rating Systems at Large
U.S. Banks,” Federal Reserve Bulletin (November 1998). They argue that
credit review organizations and processes are further enhanced
mechanisms through which common standards can be enforced across
credit officers.
21. Federal Reserve Systems Task Force on Internal Credit Risk Models, Credit
Models at Major U.S. Banking Institutions: Current State of the Art and
Implications for Assessments of Capital Adequacy, Washington, DC: U.S.
Government Printing Office, May 1998.
22. J. J. Mingo, “Policy Implications of the Federal Reserve Study of Credit Risk
Models at Major Banking Institutions,” paper presented at the Bank of
England Conference on Credit Risk Modeling and Regulatory Implications,
London, September 21–22, 1998.
23. To calculate the estimated loan loss reserve against expected losses, a
similar approach would be used, except that expected loss rates would
replace unexpected loss rates.
24. J. B. Caouette, E. J. Altman, and P. Narayanan, Managing Credit Risk: The
Next Great Financial Challenge, New York: John Wiley & Sons, 1998.
25. A. Saunders, Financial Institutions Management: A Modern Perspective, 2d ed.,
Burr Ridge, IL: Irwin/McGraw-Hill, 1997.
26. E. I. Altman and P. Narayanan, “An International Survey of Business Failure
Classification Models,” Financial Markets, Instruments and Institutions 6/2
27. E. I. Altman, “Financial Ratios, Discriminant Analysis and the Prediction of
Corporate Bankruptcy,” Journal of Finance (September 1968), 589–609.
28. E. I. Altman, T. K. N. Baidya, and L. M. R. Dias, “Assessing Potential
Financial Problems for Firms in Brazil,” Working Paper 125, New York
University Salomon Center, September 1977.
29. A. S. Sanvicente and F. L. C. Bader, “Filing for Financial Reorganization in
Brazil: Event Prediction with Accounting and Financial variables and the
Information Content of the Filing Announcement,” working paper, São
Paulo University, Brazil, March 1996.
30. P. K. Coates and L. F. Fant, “Recognizing Financial Distress Patterns Using a
Neural Network Tool,” Financial Management (Summer 1993), 142–155.
31. R. Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest
Rates,” Journal of Finance 29 (June 1974), 449–470.
32. EDF and CreditMonitor® are trademarks of KMV LLC.
33. In fact, if there are direct and indirect costs of bankruptcy (e.g., legal costs,
inventory, maintenance costs, etc.), the lender’s loss on a loan may exceed
principal and interest. This makes the payoff profile in Figure 3-7 even more
similar to that shown in Figure 3-8, where the loan may have a negative
dollar payoff.
34. R. Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest
Rates,” Journal of Finance 29 (June 1974), 449–470.
35. Ibid.
36. For a detailed analysis, see G. Gorton and A. Santomero, “Market Discipline
and Bank Subordinated Debt,” Journal of Money, Credit and Banking
(February 1990), 117–128 and M. J. Flannery and S. Sorescu, “Evidence of
Bank Market Discipline in Subordinated Debenture Yields: 1983–1991,”
Journal of Finance (September 1996), 1347–1377.
37. Most corporate bonds are traded over the counter, not publicly. Price
information is extremely difficult to get because most trades are interdealer
(bank to bank).
38. See R. A. Jarrow and D. R. van Deventer, “Practical Usage of Credit Risk
Models in Loan Portfolio and Counterparty Exposure Management,” The
Kamakura Corporation, March 15, 1999, for testing a Merton-type model
using bond quotes (spreads) for one company. They find considerable
instability in implied default probabilities. This may, in part, be due to the
use of bond quotes rather than transaction prices. See also A. Saunders,
A. Srinivasan, and I. Walter, “Price Formation in the OTC Corporate Bond
Markets: A Field Study of the Inter-Dealer Market,” Working Paper No. 9889, New York University, Department of Finance, 1998 for a discussion of
price formation in OTC corporate bond markets.
Credit Risk
39. For example, if the company’s assets are liquidated at current market values
and the resulting funds are used to meet borrowing obligations.
40. R. A. Jarrow and S. M. Turnbull, “The Intersection of Market and Credit
Risk,” paper presented at the Bank of England Conference on Credit Risk
Modeling and Regulatory Implications, London, September 21–22, 1998;
G. Delianedis and R. Geske, “Credit Risk and Risk-Neutral Default
Probabilities: Information About Rating Migrations and Defaults,” paper
presented at the Bank of England Conference on Credit Risk Modeling and
Regulatory Implications, London, September 21–22, 1998.
41. KMV does not make distinctions in the liability structure with regard to
seniority, collateral, covenants, or other parameters which distinguish the
loans. Convertible debt and preferred stock are also as long-term liabilities,
not breaking out the loan and equity components. However, users can input
whatever value of B they feel is appropriate under a specific scenario.
42. E. Ronn and A. Verma, “Pricing Risk-Adjusted Deposit Insurance: An
Option-Based Model,” Journal of Finance (September 1986), 871–896.
43. The distance from default is 3 standard deviations. KMV Credit Monitor
assumes a constant asset growth rate for all borrowers in the same market
segment, which is the expected growth rate of the market as a whole. The
rationale for this assumption is that in an efficient market, differences in
growth rates between the market and individual firms are fully discounted
(i.e., arbitraged away) and incorporated in the stock prices of the borrower.
Thus, in equilibrium there should be no difference between asset growth of
individual firms and the market. The only other adjustment to this constant
across-the-board rate is for firm-specific payouts such as dividends or interest
payments (keep in mind that the KMV Credit Monitor applies a BlackScholes-Merton option model with dividends). The adjusted number is then
applied to the implied current asset value in the distance-to-default formula.
44. Another reason for the better predictability of KMV scores over the short
horizon is the approach to calibrating the model over time. Standard &
Poor’s and Moody’s calibrate their rating to default experience over the
past 20-plus years. Their probabilities therefore reflect a cycle average view.
By comparison, KMV’s EDFs reflect strong cyclicality over the business
cycle. Some studies have shown that EDFs do not offer any advantage for
time horizons over two years; see R. Miller, “Refining Ratings,” Risk
(August 1998).
45. R. A. Jarrow and D. R. van Deventer, “Practical Usage of Credit Risk Models
in Loan Portfolio and Counterparty Exposure Management,” The
Kamakura Corporation, March 15, 1999.
46. H. Leland, “Corporate Debt Value, Bond Covenants and Optimal Capital
Structure,” Journal of Finance (September 1994), 1213–1252.
47. E. P. Jones, S. P. Mason, and E. Rosenfeld, “Contingent Claims Analysis of
Corporate Capital Structures: An Empirical Investigation,” Journal of Finance
(July 1984), 611–625.
48. C. Zhou, “A Jump Diffusion Approach to Modeling Credit Risk and Valuing
Defaultable Securities,” working paper, Washington, DC: Federal Reserve
Board of Governors, 1997.
49. R. A. Jarrow and S. M. Turnbull, “The Intersection of Market and Credit
Risk,” paper presented at the Bank of England Conference on Credit Risk
Modeling and Regulatory Implications, London, September 21–22, 1998.
50. D. Duffie and K. Singleton, “Simulating Correlated Defaults,” paper
presented at the Bank of England Conference on Credit Risk Modeling and
Regulatory Implications, London, September 21–22, 1998.
51. For a review of intensity-based models, see G. Duffee, “Estimating the Price
of Default Risk,” Review of Financial Studies (Spring 1999), 197–226.
52. D. Duffie and D. Lando, “Term Structures of Credit Spreads with
Incomplete Accounting Information,” working paper, Stanford University
Graduate School of Business, 1997.
53. H. Leland, “Corporate Debt Value, Bond Covenants and Optimal Capital
Structure,” Journal of Finance (September 1994), 1213–1252.
54. R. Anderson, S. Sunderesan, and P. Tychon, “Strategic Analysis of
Contingent Claims,” European Economic Review (1996), 871–881.
55. P. Mella-Barral and W. Perraudin, “Strategic Debt Service,” Journal of Finance
(June 1997), 531–556.
56. For example, the boundary will become stochastic if there is liquidation cost
to asset values. This gives borrowers power to renegotiate. In Merton’s
(1974) original model, there are no costs to liquidation; i.e., assets are
liquidated and paid out costlessly. See also Francis A. Longstaff and E.
Schwartz, “A Simple Approach to Valuing Risky Fixed and Floating Rate
Debt,” Journal of Finance (July 1995), 789–819.
57. H. Leland, “Agency Costs, Risk Management and Capital Structure,”
Journal of Finance (July 1998), 1213–1242.
58. V. V. Acharya and J. N. Carpenter, “Callable Defaultable Bonds: Valuation,
Hedging and Optimal Exercise Boundaries,” working paper, New York
University Department of Finance, New York, March 15, 1999.
59. The current capital requirements for supporting market risk contain a
general market risk component and a specific risk component. For example,
with respect to corporate bonds that are held in the trading book, an
internal model calculation of specific risk would include methodologies
such as spread risk, downgrade risk, and concentration risk. Each of these is
related to credit risk. The 1998 BIS market risk capital requirement contains
a credit risk component.
60. J. P. Morgan, CreditMetrics—Technical Document, New York: J. P. Morgan,
April 2, 1997. In 1998, the group that developed the RiskMetrics and
CreditMetrics products was split off into a separate company called
RiskMetrics Group.
61. For a discussion of the one-year time horizon, see the report from the
Federal Reserve System Task Force on Internal Credit Risk Models, Credit
Credit Risk
Models at Major U.S. Banking Institutions: Current State of the Art and
Implications for Assessments of Capital Adequacy, Washington, DC: U.S.
Government Printing Office, May 1998. For example, if the existence of
autocorrelation or trend over the time toward default is suspected, a longer
observation period (such as two years or more) might be appropriate.
62. As is discussed later, to calculate the VaR of a loan portfolio, default
correlations among counterparties have to be estimated.
63. This example is based on the example used in J. P. Morgan, CreditMetrics—
Technical Document, New York: J. P. Morgan, April 2, 1997, 9.
64. As is shown later, the choice of transition matrix has a substantial impact on
the VaR calculations. Moreover, the choice to apply bond transitions to
value loans raises the empirical question of how closely related bonds and
loans are.
65. Technically, from a valuation perspective, the credit event is assumed to
occur at the very end of the first year. The current version of CreditMetrics
is being expanded to allow the credit event window to be as short as three
months or as long as five years.
66. In this example, the discount rates reflect the appropriate zero-coupon rates
plus credit spreads si on A-rated loans (bonds). If the borrower’s rating
were unchanged at BBB, the discount rates would be higher, because the
credit spreads would reflect the default risk of a BBB borrower.
67. Recent empirical studies have shown that this LGD may be too high for
bank loans. A Citibank study of 831 defaulted corporate loans and 89 assetbased loans for 1970 to 1993 found recovery rates of 79 percent (or,
equivalently, LGD equal to 21 percent). Similarly, high recovery rates were
found in a Fitch Investor Service report in October 1997 (82 percent) and a
Moody’s Investor Service Report in June 1998 (87 percent). For a detailed
analysis of this issue, see E. Asarnow, “Managing Bank Loan Portfolios for
Total Return,” paper presented at the Conference on a New Market
Equilibrium for the Credit Business, Frankfurt, Germany, March 11, 1999.
68. The calculation in Table 3-6 shows the risks of a loan that have been calculated
from the perspective of its mean or expected forward value ($107.09). Using an
alternative perspective, by looking at the distribution of changes in value
around the value of the loan if the ratings continued to be BBB over the whole
loan period, the forward value is $107.55. Applying this BBB benchmark value,
the mean and the variance of the value changes are, respectively, −$0.46 and
$3.13. The VaR at the 1 percent confidence level under the normal distribution
assumption is then (2.33) × ($3.13) + (−$0.46) = −$7.75.
69. In 99 years out of 100, the capital requirements based on a VaR at a 1
percent confidence level would allow the bank to survive unexpected credit
losses on loans. Note that under the specific risk component for market risk
(which measures spread risk, downgrade risk, and concentration risk for
tradable instruments such as corporate bonds), the VaR at a 1 percent
confidence level has to be multiplied by a multiplication factor between 3
and 4 (subject to approval by the local regulator), and the sensitivity period
is 10 days instead of one year.
70. Boudoukh and Whitelaw have demonstrated in simulation exercises that,
for some financial assets, the multiplication factor can cover extreme losses
such as the mean in the tail beyond the 99th percentile. However, they also
found that the 3-to-4 multiplication factor badly underestimated extreme
losses if there are runs of bad periods, as might be expected in a major longterm economic contraction. For the detailed analysis, see J. Boudoukh, M.
Richardson, and R. Whitelaw, “Expect the Worst,” Risk (September 1995),
71. Using the simple approach to calculating a transition matrix, based on data
for 1997 and 1998. In 1997, 5.0 percent of bonds rated BBB were
downgraded to B. In 1998, 5.6 percent of bonds rated BBB were
downgraded to B. The average transition probability of being downgraded
from BBB to B is therefore 5.3 percent. See the transition matrix in Table 3-6.
See the empirical results in P. Nickell, W. Perraudin, and S. Varotto,
“Stability of Rating Transitions,” paper presented at the Bank of England
Conference on Credit Risk Modeling and Regulatory Implications, London,
September 21–22, 1998, for an analysis of the assumption of one-year
transition matrices.
72. E. I. Altman and D. L. Kao, “The Implications of Corporate Bond Ratings
Drift,” Financial Analysts Journal (May–June 1992), 64–75.
73. P. Nickell, W. Perraudin, and S. Varotto, “Stability of Rating Transitions,”
paper presented at the Bank of England Conference on Credit Risk
Modeling and Regulatory Implications, London, September 21–22, 1998.
74. RiskMetrics is developing modifications to its CreditMetrics software to
allow cyclicality to be incorporated in the transition matrix.
75. E. I. Altman and V. M. Kishore, “Defaults and Returns on High-Yield Bonds:
Analysis Through 1997,” working paper, New York University Salomon
Center, January 1998.
76. An alternative approach would be to apply KMV’s rating transition matrix,
which is calculated around KMV’s EDF scores. The correlation between
KMV’s transitions and the transitions of the ratings agencies is low.
77. L. V. Carty and D. Lieberman, Corporate Bond Defaults and Default Rates
1938–1995, New York: Global Credit Research, Moody’s Investors Service,
January 1996.
78. J. P. Morgan, CreditMetrics—Technical Document, New York: J. P. Morgan,
April 2, 1997, 30, note 2.
79. The assumption of nonstochastic interest rates is also consistent with R. C.
Merton, “On the Pricing of Corporate Debt: The Risk Structure of Interest
Rates,” Journal of Finance 29 (June 1974), 449–470. Shimko, Tejima, and van
Deventer have extended the Merton model to include stochastic interest
rates; see D. Shimko, N. Tejima, and D. R. van Deventer, “The Pricing of
Risky Debt When Interest Rates Are Stochastic,” Journal of Fixed Income
(September 1993), 58–66.
80. See also M. Crouhy and R. Mark, “A Comparative Analysis of Current
Credit Risk Models,” paper presented at the Bank of England Conference on
Credit Risk
Credit Risk Modeling and Regulatory Implications, London, September
21–22, 1998.
81. W. Treacy and M. Carey, “Internal Credit Risk Rating Systems at Large U.S.
Banks,” Federal Reserve Bulletin (November 1998).
82. P. Nickell, W. Perraudin, and S. Varotto, “Stability of Rating Transitions,”
paper presented at the Bank of England Conference on Credit Risk
Modeling and Regulatory Implications, London, September 21–22, 1998,
and Thomas C. Wilson, Credit Risk Modeling: A New Approach, New York:
McKinsey Inc., 1997; “Credit Portfolio Risk (I),” Risk (October 1997); “Credit
Portfolio Risk (II),” Risk (November 1997).
83. The unexpected loss rate could also be simulated using this type of
binominal model for a two-state world of default versus no default, rather
than a full VaR model.
84. In fact, all the probabilities in the final column of the transition matrix in
Figure 3-15 will move cyclically and can be modeled in a way similar to pCD.
85. In Thomas C. Wilson, Credit Risk Modeling: A New Approach, New York:
McKinsey Inc., 1997, and “Portfolio Credit Risk (Parts I and II),” Risk
(September and October, 1997), Equation (3.15) is modeled as a logistic
function of the form pt = 1/(1 + e−yt). This constrains p to lie between 0 and 1.
86. In Thomas C. Wilson, Credit Risk Modeling: A New Approach, New York:
McKinsey Inc., 1997, the macrovariables are modeled as levels of variables
(rather than changes in levels), and the X variables are related to their
lagged values by a second-order autoregressive process.
87. The variances and covariances of V and εit are technically calculated from
the fitted model (the I matrix). The I matrix is then decomposed using the
Cholesky decomposition I = AA′, where A and A′ are symmetric matrices
and A′ is the transpose of A. Shocks can be simulated by multiplying the
matrix A′ by a random number generator: Z ~ N (0,1).
88. Thomas C. Wilson, Credit Risk Modeling: A New Approach, New York:
McKinsey Inc., 1997; “Credit Portfolio Risk (I),” Risk (October 1997); “Credit
Portfolio Risk (II),” Risk (November 1997).
89. The precise procedure for the calculation is described in McKinsey and
Company, CreditPortfolio View Approach Documentation and User’s
Documentation, Zurich: McKinsey and Company, 1998, 80–94. Basically, it
involves the use of a shift operator (defined as the systematic risk sensitivity
parameter) along with the imposition of the constraint that the shifted
values in each row of the migration matrix sum to 1.
90. Alternatively, using a default model, and a default p/no-default 1 − p setup,
unexpected loss rates can be derived for different stages of the business
91. K. Arrow, “Le Role des valeurs boursieres pour la repartition de la meilleure
des risques,” Econometrie Colloque Internationaux du CNRS 11 (1953), 41–47.
92. J. M. Harrison and D. Kreps, “Martingales and Arbitrage in Multi-Period
Security Markets,” Journal of Economic Theory (1979), 381–408.
93. J. M. Harrison and S. R. Pliska, “Martingales and Stochastic Integrals,”
Stochastic Processes and Their Applications (August 1981), 215–260.
94. D. Kreps, “Multiperiod Securities and the Efficient Allocation of Risk: A
Comment on the Black-Scholes Option Pricing Model,” in J.J. McCall, ed.,
The Economics of Uncertainty and Information, Chicago: University of Chicago
Press, 1982.
95. For pricing of derivative assets, when the underlying asset is actively
traded, the risk-neutral price is the correct one, irrespective of investor
preferences. This is because, with an existing underlying asset, the
derivative can be perfectly hedged to create a riskless portfolio. Assuming a
portfolio is riskless, the portfolio’s expected return equals to the risk-free
96. R. K. Sundaram, “Equivalent Martingale Measures and Risk-Neutral
Pricing: An Expository Note,” Journal of Derivatives (Fall 1997), 85–98.
97. R. Litterman and Thomas Iben, “Corporate Bond Valuation and the Term
Structure of Credit Spreads,” Journal of Portfolio Management (Spring 1991),
98. For a detailed discussion, see G. Delianedis and R. Geske, “Credit Risk and
Risk-Neutral Default Probabilities: Information About Rating Migrations
and Defaults,” paper presented at the Bank of England Conference on
Credit Risk Modeling and Regulatory Implications, London, September
21–22, 1998.
99. Ibid.
100. R. C. Merton, “On the Pricing of Corporate Debt: The Risk Structure of
Interest Rates,” Journal of Finance 29 (June 1974), 449–470.
101. R. Geske, “The Valuation of Corporation Liabilities as Compound Options,”
Journal of Financial and Quantitative Analysis (November 1977), 541–552.
102. The Merton (1974) model assumes that all long-term debt is of equal
seniority and is unsecured.
103. A. Ginzberg, K. Maloney, and R. Wilner, “Risk Rating Migration and
Valuation of Floating Rate Debt,” working paper, Citicorp, March 1994.
104. B. Belkin, L. R. Forest, S. D. Aguais, and S. J. Suchower, Credit Risk Premiums
in Commercial Lending (1) and Credit Risk Premiums in Commercial Lending (2),
New York: KPMG, August 1998; B. Belkin, S. J. Suchower, and L. R. Forest,
“The Effect of Systematic Credit Risk on Loan Portfolio Value at Risk and
Loan Pricing,” CreditMetrics Monitor (1998), 17–88; B. Belkin, S. J. Suchower,
D. H. Wagner, and L. R. Forest, “Measures of Credit Risk and Loan Value in
LAS,” KPMG, Risk Strategy Practice, New York: KPMG, 1998.
105. This relationship has been described by A. Ginzberg, K. Maloney, and R.
Wilner, “Risk Rating Migration and Valuation of Floating Rate Debt,”
Working Paper, Citicorp, March 1994, and by M. Crouhy and R. Mark, “A
Comparative Analysis of Current Credit Risk Models,” paper presented at
the Bank of England Conference on Credit Risk Modeling and Regulatory
Implications, London, September 21–22, 1998.
Credit Risk
106. For example, the historic probability of a B-rated borrower transitioning
into default during the next year and thus moving from B to D in a single
107. Unlike CreditMetrics, in which the VaR measure (or unexpected loss in
value) is loan specific, these unexpected losses are specific to a rating
bucket. CreditMetrics allows for upgrade and downgrade effects on loan
value, whereas the simple risk-neutral approach assumes either default or
no default (binary decision).
108. A. Ginzberg, K. Maloney, and R. Wilner, “Risk Rating Migration and
Valuation of Floating Rate Debt,” working paper, Citicorp, March 1994.
109. Ibid.
110. Ibid.
111. KPMG Peat Marwick, Loan Analysis System, New York: KPMG Financial
Consulting Services, 1998.
112. See S.D. Aguais, L. Forest, S. Krishnamoorthy, and T. Mueller, “Creating
Value from Both Loan Structure and Price,” Commercial Lending Review
(Winter 1997), 1–10.
113. As discussed in B. Belkin, S. J. Suchower, and L. R. Forest, “The Effect of
Systematic Credit Risk on Loan Portfolio Value at Risk and Loan Pricing,”
CreditMetrics Monitor (1998), 17–88, the LAS model can also be used to
calculate VaR measures. For example, a simple VaR figure can be calculated
by using the LAS model to value the loan at the one-year (credit-event)
horizon. Alternatively, model spread volatility can be introduced by
allowing the transitions themselves to be variable (KPMG calls this Z risk).
114. KPMG Peat Marwick, Loan Analysis System, New York: KPMG Financial
Consulting Services, 1998.
115. E. I. Altman, “Measuring Corporate Bond Mortality and Performance,”
Journal of Finance (September 1989), 909–922.
116. The combination of the volatility of annual MMRs with LGDs allows one to
produce unexpected loss calculations as well. See E. I. Altman and A.
Saunders, “Credit Risk Measurement: Developments over the Last Twenty
Years,” Journal of Banking and Finance (December 1997), 1721–1742 for
117. For details, see E. I. Altman and H. J. Suggitt, “Default Rates in the
Syndicated Loan Market: A Mortality Analysis,” Working Paper S-97-39,
New York University Salomon Center, New York, December 1997.
118. A mortality rate is binomially distributed. For further discussion, see P. M.
McAllister and J. J. Mingo, “Commercial Loan Risk Management, Credit
Scoring and Pricing: The Need for a New Shared Database,” Journal of
Commercial Lending (May 1994), 6–20.
119. Most of the studies published show mortality tables that have been
calculated on total samples of around 4000 bonds and loans; see E. I.
Altman, “Measuring Corporate Bond Mortality and Performance,” Journal
of Finance (September 1989), 909–922, and E. I. Altman and H. J. Suggitt,
“Default Rates in the Syndicated Loan Market: A Mortality Analysis,”
Working Paper S-97-39, New York University Salomon Center, New York,
December 1997. However, the Central Bank of Argentina has recently built
transition matrices and mortality tables based on over 5 million loan
observations. This loan data is available on the Central Bank’s Web site
120. This is strictly true for only the simplest of the models in CreditRisk. A more
sophisticated version ties loan default probabilities to the systematically
varying mean default rate of the economy or sector of interest.
121. Credit Suisse First Boston, Credit Risk+, technical document, London/New
York, October 1997.
122. L. V. Carty and D. Lieberman, Corporate Bond Defaults and Default Rates
1938–1995, New York: Global Credit Research, Moody’s Investors Service,
January 1996.
123. Credit Suisse First Boston, CreditRisk+, technical document, London/New
York, October 1997.
124. Michael B. Gordy, “A Comparative Anatomy of Credit Risk Models,” paper
presented at the Bank of England Conference on Credit Risk Modeling and
Regulatory Implications, London, September 21–22, 1998.
125. H. U. Koyluoglu and A. Hickman, A Generalized Framework for Credit Risk
Portfolio Models, New York: Oliver, Wyman and Co., September 14, 1998.
126. M. Crouhy and R. Mark, “A Comparative Analysis of Current Credit Risk
Models,” paper presented at the Bank of England Conference on Credit Risk
Modeling and Regulatory Implications, London, September 21–22, 1998.
127. For a detailed discussion of the MTM and DM approaches, see Bank for
International Settlement (BIS), Basel Committee on Banking Supervision,
Credit Risk Modelling: Current Practices and Applications, Basel, Switzerland:
Bank for International Settlement, April 1999, 17, 22.
128. For a discussion of multifactor models, see Reto R. Gallati, “Empirical
Application of APT Multifactor-Models to the Swiss Equity Market,” Basic
Report, Zurich: Credit Suisse Investment Research, September 1993, and
M. J. Gruber, Modern Portfolio Theory and Investment Analysis, 5th ed., New
York: John Wiley & Sons, 1998.
129. For a discussion, see E. I. Altman and A. Saunders, “Credit Risk
Measurement: Developments over the Last Twenty Years,” Journal of
Banking and Finance (December 1997), 1721–1742.
130. Reto R. Gallati, “Empirical Application of APT Multifactor-Models to the
Swiss Equity Market,” basic report, Zurich: Credit Suisse Investment
Research, September 1993
131. S. Kealhofer, “Managing Default Risk in Derivative Portfolios,” in Derivative
Credit Risk: Advances in Measurement and Management, London: Renaissance
Risk Publications, 1995.
132. The EDFs of the KMV model vary from 0 to 20%. By allocating EDFs into score
ranges or categories, a transition matrix can be generated based on EDF scores.
Credit Risk
133. In recent documentation, KMV has applied a multiple of 10; thus, capital =
ULp ⋅ 10.
134. A standardized return is a current return divided by its estimated standard
deviation after subtracting the mean return. A standardized normal
distribution has a mean of zero and a standard deviation of unity, (x − µi)/σi
→ N(0,1)
135. It can be argued that correlations should be measured between loans, not
borrowers. For example, a low-quality borrower with a highly secured loan
(e.g., collateralized, guarantees, etc.) would find the loan rated more highly
than the borrower as a whole.
136. The calculation has been done by backward calculation of the probabilities
of the worst outcome: the worst loan outcome, then the second-worst, and
so forth.
137. Technically, the correlation matrix Σ among the loans is decomposed using
the Cholesky factorization process, which finds two matrices A and A′ (its
transpose) such that I = AA′. Asset return scenarios y are generated by
multiplying the matrix A′ (which contains memory relating to historical
correlation relationships) by a random number vector z; i.e., y = A′z.
138. D. Duffie and K. Singleton, “Simulating Correlated Defaults,” paper
presented at the Bank of England Conference on Credit Risk Modeling and
Regulatory Implications, London, September 21–22, 1998 provides a
discussion of various algorithms to estimate default correlation intensities
and an extensive review of the intensity-modeling-based research.
139. The current regulations for the BIS internal model for market risk require
that the bank’s internal VaR be multiplied by a factor of 3 to 4, subject to
approval of the local regulator. Intuitively, this multiplier can be regarded as
a stress-test multiplier accommodating outliers in the 99 percent tail of the
distribution. If, in backtesting a model, regulators or auditors find that the
model underestimated VaR on fewer than 4 out of the past 250 days, the
VaR multiplier remains at its minimum value of 3. If 4 to 9 days of
underestimated risk are found, the multiplier is increased to a range of 3.4
to 3.85. If more than 10 daily errors are found, the multiplication factor for
the internal VaR is set at 4. The multiplier is subject to other qualitative
restrictions, which influence the multiplier granted by the regulator.
140. This assumption is still optimistic. Not even the rating agencies have
current default histories going back that far. Most financial organizations
can provide perhaps two or three years’ usable data for the loans they grant.
141. C. W. J. Granger and L. L. Huang, “Evaluation of Panel Data Models: Some
Suggestions from Time-Series,” Discussion Paper 97-10, University of
California, Department of Economics, San Diego, 1997.
142. Mark Carey, “Credit Risk in Private Debt Portfolios,” Journal of Finance
(August 1998), 1363–1387.
143. J. A. Lopez and M. R. Saidenberg, “Evaluating Credit Risk Models,” paper
presented at the Bank of England Conference on Credit Risk Modeling and
Regulatory Implications, London, September 21–22, 1998.
144. For details, see ibid.
145. The analogy with backtesting market risk models using time-series data is
linked to how representative the past period is (i.e., the last 250 days under
the BIS rules).
146. G. Stahl, “Confidence Intervals for Different Capital Definitions in a Credit
Risk Model,” paper presented at Center for Economic Policy Research
(CEPR) Conference, London, September 20, 1998.
147. Mark Carey, “Credit Risk in Private Debt Portfolios,” Journal of Finance
(August 1998), 1363–1387.
148. Reto R. Gallati, “Switzerland Money Markets,” in Nick Battley, ed., The
European Bond Markets: An Overview and Analysis for Issuers and Investors, 6th
ed., Cambridge, MA: McGraw-Hill, 1997, 1373.
149. Paul Vienna, An Investor’s Guide to CMOs, New York: Salomon Brothers,
1986 and Gregory J. Parseghian, “Collateralized Mortgage Obligations,” in
Frank Fabozzi, ed., The Handbook of Fixed-Income Securities, 3d ed.,
Homewood, IL: McGraw-Hill, 1991.
150. Institute of International Finance (IIF), Recommendations for Revising the
Regulatory Capital Rules for Credit Risk: Report of the Working Group on Capital
Adequacy, Washington, DC: Institute of International Finance, 1998.
151. International Swaps and Derivatives Association (ISDA), Credit Risk and
Regulatory Capital, New York/London: International Swaps and Derivatives
Association, March 1998.
152. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, A New Capital Adequacy Framework: Consultative Paper Issued by
the Basel Committee on Banking Supervision for Comment by 31 March 2000,
Basel, Switzerland: Bank for International Settlement, June 1999.
153. See Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, International Convergence of Capital Measurement and Capital
Standards, Basel, Switzerland: Bank for International Settlement, July 1988.
154. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Credit Risk Modelling: Current Practices and Applications, Basel,
Switzerland: Bank for International Settlement, April 1999.
155. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, A New Capital Adequacy Framework: Consultative Paper Issued by
the Basel Committee on Banking Supervision for Comment by 31 March 2000,
Basel, Switzerland: Bank for International Settlement, June 1999, 14, para.
156. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Operational Risk, Consultative Document: Supporting Document to
the New Basel Capital Accord, Issued for Comment by 31 May 2001, Basel,
Switzerland: Bank for International Settlement, January 2001.
157. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Measurement of Banks’ Exposure to Interest Rate Risk, Basel,
Switzerland: Bank for International Settlement, April 1993.
Credit Risk
158. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, A New Capital Adequacy Framework: Consultative Paper Issued by
the Basel Committee on Banking Supervision for Comment by 31 March 2000,
Basel, Switzerland: Bank for International Settlement, June 1999, para. 21ff;
The Standardized Approach to Credit Risk, Consultative Document: Supporting
Document to the New Basel Capital Accord, Issued for Comment by 31 May 2001,
Basel, Switzerland: Bank for International Settlement, January 2001.
159. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, A New Capital Adequacy Framework: Consultative Paper Issued by
the Basel Committee on Banking Supervision for Comment by 31 March 2000,
Basle, Switzerland: Bank for International Settlement, June 1999, para.
150ff.; The Internal Ratings-Based Approach, Consultative Document: Supporting
Document to the New Basel Capital Accord, Issued for Comment by 31 May 2001,
Basel, Switzerland: Bank for International Settlement, January 2001.
160. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, The Internal Ratings-Based Approach, Consultative Document:
Supporting Document to the New Basel Capital Accord, Issued for Comment by 31
May 2001, Basel, Switzerland: Bank for International Settlement, January
2001, para. 24ff.
161. Ibid., para. 33ff.
162. Ibid., paras. 52ff and 392ff.
163. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, A New Capital Adequacy Framework: Consultative Paper Issued by
the Basel Committee on Banking Supervision for Comment by 31 March 2000,
Basel, Switzerland: Bank for International Settlement, June 1999, paras. 61ff.,
181, and 653ff.
164. Ibid., para. 404.
165. Ibid.
166. Ibid., para. 80ff.
167. Ibid., para. 516ff.
168. Ibid., para. 546ff.
169. Ibid., para. 503ff.
170. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, “Update on Work on the New Basel Capital Accord,” Basel
Committee Newsletter 2 (September 2001).
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Operational Risk
Operational risk is not a new risk. In fact, it is the first risk a bank must
manage, even before it makes its first loan or executes its first trade. However, the idea that operational risk management is a discipline with its
own management structure, tools, and processes, much like credit or market risk, is new and has evolved over the last five years.
In 1998, the Basel Committee on Banking Supervision published a
consultative paper related to operational risk.1 Operational risk is an accepted part of sound risk management practice in modern financial
markets. According to the BIS paper, the most important types of operational risk involve breakdowns in internal controls and corporate governance. Such breakdowns can lead to substantial financial losses through
error, fraud, or failure to perform obligations in a timely manner, or can
cause the interests and existence of the bank to be compromised in some
other way. This may include dealers, lending officers, or other staff
members exceeding their authority or conducting business in an unethical or risky manner. Other aspects of operational risk include the major
failure of information technology systems, or events such as fires or
other disasters.
Most financial institutions assign primary responsibility for managing operational risk to the business line head. Those banks that are developing measurement systems for operational risk are also often
attempting to build incentive structures and processes for sound operational risk management practice by business managers. These incentive
structures can take the form of allocating capital for operational risk, in283
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cluding operational risk measurement in the performance evaluation
process, or requiring business line management to present operational
loss details and resultant corrective action directly to the bank’s highest
levels of management.
Such a framework for managing operational risk is only in its early
stages of development. Awareness of operational risk as a separate risk
category is present and enforced by most auditors, as they include operational risk statements in their annual audit reports. Only a few sophisticated banks currently measure and report this risk on a regular basis,
although many track operational performance indicators, analyze loss experiences, and monitor audit and supervisory ratings.
Significant conceptual issues and data needs have been identified
that should be addressed to develop general measures of operational risk.
Unlike market and perhaps credit risk, operational risk factors are largely
internal to the bank, and a clear mathematical or statistical link between
individual risk factors and the likelihood and size of operational loss
(earnings volatility) does not yet exist. Experience with large losses is infrequent, and many banks lack a time series of historical data on their own
operational losses and the causes of these losses. While the industry is far
from converging on a set of standard models, such as are increasingly
available for market and credit risk measurement, the banks that have developed or are developing models rely on a surprisingly similar set of risk
factors. Those factors include internal audit ratings or control self-assessments; operational indicators such as volume, turnover, or rate of errors;
loss experience; and income volatility.
One potential benefit of a formal approach to operational risk is that
it becomes possible to develop incentives for business managers to adopt
sound risk management practices through capital allocation charges, performance reviews, or other mechanisms. Many banks are also working
toward some form of capital allocation as a business cost in order to create
a risk pricing methodology.
Financial institutions are convinced that operational risk management programs protect and enhance shareholder value. Operational risk
management as a distinct internal function with its own process, structure, tools, and measures is emerging, consisting of a set of integrated
processes, tools, and mitigation strategies. This new trend is bringing a
formal process and increased transparency to one of the oldest forms of
risk. The key considerations are as follows:
The creation of operational risk management programs has been
driven by a combination of management commitment, need for
an understanding of enterprisewide risks, a perceived increase in
exposure to operational risk and risk events, and regulatory
Operational Risk
There is consensus on the core definition of operational risk:
the risk of direct or indirect loss resulting from inadequate or
failed internal processes, people, and systems or from external
Methodologies are evolving to quantify operational risk capital.
While progress is being made, there is no consensus on approach,
and methodologies are not yet used as a basis for decision
Lacking any guidance from the regulatory side, each firm may have
developed its own understanding of operational risk management. Still,
five stages of development of an operational risk management framework
can be differentiated, which may help companies starting a program prioritize their efforts:
1. Senior management commitment. Senior management is committed to the vision that a new approach has merit.
2. Perceived increase in operational risk. Due to growing service
businesses and diffusion of market and credit risks, operational
risk receives increased attention from different interested
groups, such as investors, regulators, clients, etc.
3. Reaction to major loss events. Losses have occurred internally or
to others and forced senior managers to take action.
4. Focus on enterprisewide risk management. After the development
of processes for market and credit risk management, operational
risk is the next logical step.
5. Regulatory attention. The industry responds and moves ahead
of expectations.
The operational form of risk is one of the most significant dimensions confronted by all businesses, financial and nonfinancial institutions alike.
Historically, at least within the financial services industry, the more
widely understood financial risks, such as market and credit risk, have
taken precedence at both senior management and board levels. Investment decisions have focused on enhancing management’s ability to identify, measure, monitor, and control traditional financial risks, with
increasing emphasis on capabilities to deliver information on a real-time
basis. More recently, however, operational risk has become increasingly
prominent on the agenda of regulators, investors, and management.
4.2.1 Drivers of Operational Risk Management
Highly publicized organizational failures that have caught much media attention have increased the realization by management and regulators that
many of the most severe operational losses could happen again almost
anywhere. This prominence is fueled by a number of linked and equally
important factors:
Continuing changes in the regulation of the financial services
sector have increased the focus on the prudential aspects of
operational risk, including capital sufficiency and operational,
control, and management effectiveness. Of particular interest is
the introduction of personal accountability by management and
boards of directors in more and more jurisdictions.
Competitive pressures resulting from the smaller profit margins
in traditional financial risk management products have increased
the drive to innovate with ever more complex, nonstandard
products or delivery mechanisms in less time. Each innovation, in
its unique way, stretches to the limit the boundaries of existing
business processes, which have largely been designed for high
volume and relatively straightforward products and services.
This continually changing product development and delivery
process continues to undermine the capability of an organization
to design and build a stable management infrastructure. What
must be guarded against is a purely reactive, piecemeal evolution
of not only the technology and supporting processes but, perhaps
more important, the skill base of those charged with the
responsibility of managing the new business model.
Consolidation among financial service providers has created
larger and more closely aligned institutions. These institutions
are more complex as well as interconnected through internal and
external organizations and substantial transactions. Accordingly,
the frequency and complexity of operational problems will likely
increase within institutions and on a concurrent basis with
external organizations.
Increasing use of technology in both the distribution and processing
of transactions has increased the speed with which operational
problems manifest themselves. To the extent that organizations use
manual processes and “workarounds” that are neither efficient nor
scalable, the probability of operational risks is further increased.
Improved technology may mitigate this risk to some extent but,
where mismanaged, can only serve to emphasize the impact of
inadequacies. Technology, though on the whole an aid to greater
efficiency and effectiveness, has also increased the capacity of
operations, thus magnifying the effect of operational breakdown.
Operational Risk
Shareholders increasingly expect compensation for investments and
the risks associated with investment decisions. Management is now being
asked to justify the nature and extent of capital invested in the business
and to make appropriate disclosures of risk management and capital allocation processes in annual financial statements. The pressure to measure
and disclose risk in capital terms will continue to increase as shareholder
sophistication increases.
In a marketplace as ever changing and unpredictable as global financial services, the real challenge is to generate a management momentum equal in its dynamics to that of the environment so that processes and
technology infrastructure can be consistently designed and redesigned to
meet the needs of existing business. Figure 4-1 highlights the drivers of
operational risk.
There are numerous examples of the complexity and risks associated
with doing business in the 1990s, not least of which is the Barings collapse.
F I G U R E 4-1
Drivers of Operational Risk.
Risk awareness
Influencing factors
Increasing sophistication of
awareness and approaches
External pressure
Market events
and impact
Clarity of roles
BIS capital
Identification and
assessment of
operational risks
Motivating and
managing change
Reorganization of
structures Optimization of
Cost efficiencies
Allocation of
Measurement of
in business
Reallocation of
Control and
(See the case study on Barings in Chapter 6.) This, and a few others, are
classic examples of operational failures where the ultimate price was paid
by the shareholders and the institutions. Although many control failures
and procedural breakdowns contribute to a collapse on this scale, it highlights the role that management can play in limiting the impact of operational failure. In the case of Barings, it is acknowledged in the final
analysis that management, with limited resources available, had not selected the appropriate business segment on which to focus attention. Accumulations of competencies, supernormal profits, and unexpected losses
are indicators of potential operating abnormalities. Management must simultaneously encourage good performance and continually question the
validity of that performance.
4.2.2 Operational Risk and Shareholder Value
Operational risk management initiatives protect and enhance shareholder
value. The evidence is qualitative rather than quantitative. The primary
benefit received from an operational risk management program is the protection of shareholder value, encompassing internal awareness of operational risk, protection of reputation, and decreased levels of operational
An effective operational risk management framework can add value
by improving competitive advantage and reducing the level of losses from
large events that can imperil financial condition and from smaller, more
frequent incidents.
Risk-adjusted measures such as economic value added (EVA) and
shareholder value added (SVA) are one way to measure the benefit from
improved operational risk management.
EVA = net result − (risk capital × required interest rates)
EVA is the numerator of RAROC. It measures the absolute value of
an investment generated in excess of the target profitability. A business
unit with a positive EVA adds to the value of an institution.
SVA = 冱 NPV (EVAt)
SVA measures the added value of an investment to the shareholder.
An investment should be carried out if SVA is positive.
The quantification of operational risk allows us to express the loss
(or potential loss), which reduces the net result. Thus, it is easy to figure
out the added value of operational risk prevention in the context of EVA
and SVA measures.
Operational Risk
A common definition for operational risk is emerging. The debate on how
to define operational risk has at times overshadowed the debate on how to
manage it. How can institutions be expected to manage operational risk if
they cannot define it? Many banks have their own internal definition of
operational risk, and the great majority of them are satisfied with that definition.
In reviewing those definitions, analyzing common classifications,
and eliminating linguistic, cultural, and organizational differences, it becomes obvious that there is a common core operational risk definition,
Operational risk is the risk of direct or indirect loss resulting from inadequate or failed internal processes, people, and systems or from external
This definition is a comprehensive, positive, and forward-looking
statement that can be adapted by firms to reflect their own circumstances.
An important distinction of the BIS definition is that it focuses on the
sources of losses. But at an industry level this does express the core operational risk factors of most firms (and can facilitate exchange of information). It should also be understood that this definition is not intended to
include defaults or changes to financial markets that are otherwise covered in the scope of market and credit risks.
The key distinction of the BIS definition is that it focuses on the impact of operational losses. This is a fundamental difference in the conceptual approach to creating a definition.
According to the BIS consultative paper, there is at present no
agreed-upon universal definition of operational risk. A common definition of operational risk is any risk not categorized as market or credit risk.
Other institutions have defined it as the risk of loss arising from various
types of human or technical error. Still others associate operational risk
with settlement or payment risk and business interruption, administrative, and legal risks. Several types of events (settlement, collateral, and
netting risks) are seen by some institutions as not necessarily classifiable
as operational risk and may contain elements of more than one type of
risk. The institutions participating in the study all see some form of link
between credit, market, and operational risk. In particular, an operational
problem with a business transaction (for example, a settlement failure)
could create market or credit risk. While most banks view technology risk
as a type of operational risk, some view it as a separate risk category with
its own discrete risk factors.
The majority of banks associate operational risk with all business
lines, including infrastructure, although the mix of risks and their relative
magnitude may vary considerably across businesses. Operational risk is
tracked in business lines with high volume, high turnover (transactions/time), a high degree of structural change, and/or complex support
systems. Operational risk is viewed as having a high potential impact on
business lines with those characteristics, especially if the businesses also
have low margins, as occurs in certain transaction-processing and payment system activities.
Operational risk for any institution arises from the influence and interaction of internal and external events on the people, processes, and
technology applied to the business processes within that institution.
Given that institutions are generally unique in the way they combine people, processes, and technology, it is difficult if not impossible to create a
single generic definition for what constitutes operational risk.
Traditional definitions of operational risk are skewed and focused
primarily on the negative aspects of risk, including the potential that, for
one reason or another, business processes will be disrupted, resulting in a
direct or indirect financial loss. Loss-incurring events may be driven by
factors such as inadequate or failed information systems, inadequate or
failed processes or controls, human error or fraud, or even unforeseeable
natural catastrophes. Direct loss refers to losses on current earnings. Indirect loss refers to loss of potential earnings—for example, due to operational impediments to expanding the business or customer attrition
resulting from reputation problems. This type of definition is backward
looking, and historic information is of limited use to prevent future losses
or to foretell threats to the existence of the organization.
Less traditional and potentially more strategic definitions of operational risk incorporate the positive view of risk (see Figure 4-2). Rather
than viewing risk only as financial loss from market/credit risk exposures, operational risk includes consideration of the failure of operational
processes or strategic investment decisions to optimize returns or financial gains. This definition introduces the concept of opportunity cost.
From a theoretical and academic standpoint, it is desirable to clarify
discussions about operational risk and to identify and differentiate operational risk from all of the themes and categories discussed in previous
chapters. This enables us to allocate and differentiate all risk definitions
within a holistic framework and avoid the overlapping of well-defined
risks. However, it is too big an undertaking for the purpose of this book,
and we will restrict the identification and differentiation of operational
risks to market and credit risks. Other risks, such as settlement, liquidity,
and strategic risks, are summarized under “others” (see Table 4-1).
Analyzing recent losses, we are tempted to allocate negative developments to causes and impacts. Causes could be the undesirable deviation from an expected outcome, and impacts would be the risk, as it
usually results in a loss that can be expressed in a value term. Many definitions do not explore this differentiation. Other definitions do not make a
Operational Risk
F I G U R E 4-2
Definition of Operational Risk as an Opportunity Instead of a Threat.
distinction and mix both dimensions, which makes identification and differentiation difficult. This is especially true for operational risk, as the
process of building up loss databases requires a formal structure to categorize the losses. Quantitative analyses based on mixed definitions make
less sense.
The analyses of losses, e.g., in the cases of Barings, Sumitomo, or
Metallgesellschaft, tend to define losses as market risks. In the context of
the cause-impact relationship, the definition of operational risk becomes
meaningful, as the fundamental principles of internal control, segregation
of dues, due diligence, etc. had been severely neglected in these cases.
For the purpose of this book, we will use the approach highlighted in
Table 4-1. The definition of operational risk distinguishes between direct
and indirect impacts from operational risk causes. The impact might be
manifested in a market risk, resulting in a loss or profit. The matrix is
based on the assumption that it is possible to identify the causes of operational risks, such as unexpected losses from internal errors; false assessment of situations, strategies, and external events; and so on. Sloppy
oversight of counterparty risks can result in credit risk losses that could
have been prevented by an appropriate internal control system and management culture. The direct impacts will immediately hit the P&L statement and the balance sheet at the moment of their occurrence, and the
T A B L E 4-1
Definition Matrix for Identifying and Measuring Risk Based on Impact and Cause
Direct Appearance of Operational Risk
Loss from
Change in
Loss from
Change in
Market Value
Operational Losses in Form of
Other Losses
Extra Costs
Loss of
of Operational
Risk in Form of
Loss of Market
Value (Including
Reputational Risk)
Unsafe or erroneous
counterparty information
Unsafe or erroneous
information regarding
market development
Errors in areas such as:
Human resources
External events
Others, such as false
assessment regarding:
SOURCE: Modified from Hans Geiger and Jean-Marc Piaz, “Identifikation und Bewertung von operationellen Risiken,” in Henner Schierenbeck (ed.), Handbuch Bank-Controlling, 3d ed., Wiesbaden,
Germany: Gabler Verlag, 2000.
Operational Risk
indirect losses will result indirectly in discounted values of future expected cash flows. One example is the higher refinancing rates paid
through the treasury department because the bank’s counterparty risk is
considered high. This decreases the bank’s profit through higher costs,
and, because of the low rating, the bank’s market valuation is lower than
it would be with a higher credit rating (higher discount rate including
higher credit spread).
How does the matrix impact the definitions? It helps to distinguish
between the causes and impacts and among the relationships between the
different risk categories, creating an allocation of risk. The following examples will clarify the matrix:
A constrained definition of credit risk in the form of a negative
change in creditworthiness resulting in potential credit loss—and
thus requiring a higher risk premium—which is based on unsafe
or erroneous information on counterparties (first entry in first
row of matrix). According to the preceding definition, this type of
operationally caused unexpected credit loss would not be a credit
risk subject to capital support.
A day trader taking market risks by holding outdated positions
due to failing processes and infrastructure. An outdated system
that is reporting T+2 information through a batch process is
The definition of operational risk by the Bank of International Settlement is subject to controversy. (See the preceding discussions.) The BIS defines operational risk as “the risk of direct or indirect loss resulting from
inadequate or failed internal processes, people, and systems or from external events.” While this definition includes legal risk, strategic and reputational risk are explicitly not included for the purpose of minimum
regulation. We consider reputational risk as an integral part of the operational risk definition to be consistent with the BIS definition as an integrating framework. For the purpose of an international and regulatory binding
definition, in this book we use the BIS definition of operational risk. We assume that the BIS (given all the feedback from the industry) will modify the
definition and add reputational risk as a component of the definition.
A first step in understanding the regulatory approach to operational risk
is to read the relevant supplement of the consultation document for the revised Capital Accord issued by the Basel Committee of the Bank for International Settlement in January 2001.3 Most remarkable is how much
guidance the Committee is asking for from industry practitioners. Several
times during the course of the document, the BIS requests feedback on a
variety of topics. Some issues involved are very basic. For example, the
discipline of operational risk management is so new that the BIS has only
recently settled on a “final” definition of operational risk4 (see Figure 4-3).
This definition includes legal risk but not strategic or reputational risks.
However, while the BIS may have heroically settled on a definition, the industry is still arguing over exactly what it means and how it relates to
their attempts to put operational risk management on firm ground. While
this definition has eliminated some sources of uncertainty (for example, it
does not include the risks arising from botched business or strategic decisions, which were implied in earlier discussions), others remain. For example, the BIS specifically excludes reputational risk. Reputational risk is
one of the key hazards for financial services companies, for which a good
name is often a key intellectual property asset. Damage to that good name
F I G U R E 4-3
Definition of Operational Risk Based on the BIS Approach.
Internal processes
Human factors
Direct and
External events
Operational Risk
is one of the most difficult risks to overcome: you usually can’t pay a fine
or take a charge (no matter how painful) that will quickly reduce the risk
to your firm’s reputation. So quantifying and capitalizing reputational
risk is no easy matter—and does not sit easily with attempts to quantify
and capitalize many other forms of operational risk, such as systems failures or payment errors. That in turn has led to suggestions that reputational risk should not in fact be considered operational risk. While the BIS
has settled on a definition of operational risk, the industry is still arguing
over exactly what it means.
Part of the answer is that operational risk measurement is not the
same thing as operational risk management. Quantifying those operational
risks that lend themselves to quantification and neglecting the rest does
not constitute best practice in operational risk management. As we will
later discuss, and as the BIS consultation document acknowledges, there is
a pronounced need for greater discussion (and management) of the qualitative aspects of operational risk.
So far, however, the banking industry has largely focused its efforts
on coming up with measurement techniques that will allow it to take advantage of the “evolutionary” capital regime proposed by the Basel Committee on banking risks. But the best measurement techniques and capital
models in the world will not reduce operational risks unless they are used
in coordination with inherently solid management processes. While these
techniques may assist firms in reducing their capital charges, allowing
them to deploy their hard currency elsewhere, they remain exposed to
risks that can harm (if not destroy) their reputations, or severely impair
their liquidity and ability to meet financial commitments.
Most risks to financial firms can be divided into expected losses
(covered by reserve provisions), unexpected losses (covered by regulatory
and economic capital), and catastrophic losses that must simply be prevented by internal controls or transferred using insurance or alternative
risk transfer (ART) instruments. The problem in devising rules for the capitalization of operational risk is that as yet it is quite unclear what proportion and type of operational risks fall into each category—and the
boundaries keep moving as the industry changes.
To take a classic example, the management of Barings Bank was reportedly warned of the dangers of putting Nick Leeson in charge of both
trading and settlement at a remote outpost with little additional oversight.
They clearly felt that the operational risk involved was minor—but were
proved dramatically wrong when it came to light in 1995 that Leeson had
built up, and systematically concealed, a huge loss-making position. The
operational risk was catastrophic. The most effective control over that risk
would have been a change in organizational structure, not capitalization.
Today, a number of firms offer “rogue trader” insurance, which could be
viewed as a form of capitalization against operational risk. However, it is
unlikely that they would agree to provide cover to companies with internal controls as botched as those of Barings. So operational risk management, in this case, is about internal controls, not about quantification and
capitalization. (For details, see the analysis of Barings in Chapter 6.)
More generally, it is important to consider quantification and capitalization of operational risk as just two of many tools in the establishment
of a viable program. The reality is that all financial organizations need to
consider at least rudimentary approaches to operational risk capital, even
where these do not lead to regulatory benefits; while operational risks are
perhaps less tangible than market or credit risks, they have been responsible for some of the biggest losses in history. (See the discussion of case
studies in Chapter 6.)
The operational risk function is responsible for the development of
firmwide operational risk policies, frameworks, and methodologies created to advise the business units. In this emerging model, the most common responsibilities for this new function are:
Determining operational risk policies and definition
Developing and deploying common tools
Establishing indicators
Assessing benefits of programs
Analyzing linkages to credit and market risk
Consolidating cross-enterprise information
In addition, operational risk managers focus on cross-enterprise operational risk management initiatives such as developing economic capital methodologies and building loss databases. They can also be charged
with the management of the firm’s portfolio of operational risks. Depending on the relationship with the business units, they may consult or participate in operational risk management projects with business units.
There are a variety of stand-alone tools that companies are using to manage operational risk.
Operational risk management is developing a comprehensive set of
tools for the identification and assessment of operational risk. Individual
firms use a wide variety of techniques grouped around five topics: risk
and self-assessment, risk mapping, risk indicators, escalation triggers, and
loss event databases. The tool currently most valued and used is self-assessment (or risk assessment). However, the tool that most financial institutions are investigating, and that is next in line for development, is the
internal loss database.
Operational Risk
Methodologies to quantify operational risk capital are improving,
but firms are not satisfied with the results so far. The majority of the financial institutions are in the process of developing a measure of economic capital for operational risk. However, the gap between what most
firms want to achieve and what they are able to achieve remains large. The
focus of current research and development efforts is the structural approach and the behavioral incentives that are created. As a consequence,
operational risk capital measures are not yet used to drive economic decision making.
A healthy range of approaches are being applied along a continuum
between top-down and more risk-based bottom-up approaches. These
methodologies often rely on actual data, can quantify the level of exposure
to each type of risk at the business line level, and react to changes in the
control environment and actual operational risk results. Since no single
approach is satisfactory, most firms currently use multiple methodologies
to obtain a result. Overall, there is little movement toward risk-based and
bottom-up methodologies (see Figure 4-4). To move forward, the industry
will need to overcome three major obstacles: data, measurement, and
management acceptance.
A framework for operational risk is emerging that consists of a set of
integrated processes, tools, and mitigation strategies. Some key components contribute the most to the operational risk framework and reflect
the company’s culture, including the style of decision making, the level of
formal processes, and the attributes of the core business:
F I G U R E 4-4
Credit Risk: Bottom-Up Versus Top-Down Approaches.
Aggregative models
(generally applied to broad lines
of business, top-down
Top-down approaches
• Historically charge off volatility
Structural models
Market risk
Credit risk
Operational risk
Bottom-up approaches
1. Definition of credit loss
• Default mode (DM)
• Mark-to-market (MTM)
2. Internal credit ratings
3. Valuation of loans
4. Treatment of creditrelated optionality
5. Parameter specification/
6. PDF computation
• Monte Carlo simulation
• Mean/variance
• Historical simulation
7. Capital allocation policy
Strategy. Risk management starts with the overall strategies
and objectives of the institution and the subsequent goals for
individual business units, products, or managers. This is
followed by identification of associated inherent risks in
strategies and objectives. Both negative events (e.g., a major loss
that would have a significant impact on earnings) and
opportunities (e.g., new products that depend on taking
operational risk) are considered. As a result, a firm can set its risk
tolerance—specifically, what risks the company understands, will
take, and will manage versus those that should be transferred to
others or eliminated. It is the basis for decision making and a
reference point for the organization.
Risk policies. Risk strategy is complemented by operational risk
management policies, which are a formal communication to the
organization as a whole on the approach to, and importance of,
operational risk management. Policies typically include a
definition of operational risk, the organization approach and
related roles and responsibilities, key principles for management,
and a high-level discussion of information and related
Risk management process. This sets out the overall procedures for
operational risk management:
Controls. Definition of internal controls, or selection of alternate
mitigation strategy, such as insurance, for identified risks.
Assessment. Programs to ensure that controls and policies are
being followed and to determine the level of risk severity. These
may include process flows, self-assessment programs, and audit
Measurement. A combination of financial and nonfinancial
measures, risk indicators, escalation triggers, and economic capital
to determine current risk levels and progress toward goals.
Reporting. Information for management to increase awareness
and prioritize resources.
Risk mitigation. These are specific controls or programs designed
to reduce the exposure, frequency, severity, or impact of an event
or to eliminate (or transfer) an element of operational risk.
Examples include business continuity planning, IT security,
compliance reviews, project management, and merger integration
and insurance. A variety of techniques are used to control or
mitigate operational risk. As discussed later, internal controls and
the internal audit process are seen as the primary means of
controlling operational risk. Financial institutions have a variety
of other possibilities. A few banks have established some form of
Operational Risk
operational risk limits, usually based on their measures of
operational risk, or other exception-reporting mechanisms to
highlight potential problems. Some banks surveyed cited
insurance as an important mitigator for some forms of
operational risk. It is a standard accounting procedure to
establish a provision for operational losses similar to traditional
loan loss reserves now routinely maintained. Several banks are
also exploring the use of reinsurance, in some cases from captive
subsidiaries, to cover operational losses.
Operations management. This refers to the day-to-day processes,
such as front- and back-office functions, technology, performance
improvement, management reporting, and people management.
Every process has a component of operational risk management
embedded in it.
Culture. There is always a balance between formal policies and
culture or the values of the people in the organization. In
operational risk, cultural aspects such as communication, the tone
at the top, clear ownership of each objective, training,
performance measurement, and knowledge sharing all help set
the expectations for sound decision making.
In addition, the integration with market and credit risk in an enterprisewide risk management framework is noted, as well as alignment
with the needs of the stakeholders, e.g., customers, employees, suppliers,
regulators, and shareholders.
The evolution of operational risk management practices varies in a number of ways depending on the company culture and operational risk event
history. Although the surveyed companies had different experiences, after
synthesizing the results we can see that there are five stages in the evolution of operational risk management (see Table 4-2). This should be helpful to companies developing operational risk initiatives.
Stage 1: traditional approach. Operational risks have always existed
and are traditionally managed by focusing primarily on self-control
and internal controls. This is the responsibility of individual
managers and specialist functions, with periodic objective review
by internal auditors. Usually, there is not a formal operational risk
management framework such as is discussed in this book.
Stage 2: awareness. The second stage in the evolution begins with
the commitment of senior management to make the organization
T A B L E 4-2
Stages of Operational Risk
nt Stages
Trend of Developme
Traditional approach
Stage 1
Internal control
Reliance on internal
Individual mitigation
Reliance on quality of
people and culture
Stage 2
Operational risk
Governance structure
Definition policy
Stage 3
Clear vision and goals
for operational risk
Process maps/
Escalation triggers
Early indicators
Early indicators
Begin collection of event
data and establishment
of value proposition
Begin collection of event
data and establishment
of value proposition
Top-down economic
capital models
Top-down economic
capital models
Stage 4
Comprehensive loss
Set quantitative goals for
Predict analysis and
leading indicators
Risk-based economic
Active operational
Stage 5
Full, linked set of tools
Cross-functional risk
Correlation between
indicators and losses
Insurance linked with risk
analysis and capital
Risk-adjusted returns
linked to compensation
Operational Risk
more proactive in its understanding of operational risk and the
appointment of someone to be responsible for operational risk. To
gain awareness, there must be a common understanding and
assessment of operational risk. This assessment begins with the
formulation of an operational risk policy based on the business
strategy, a definition of operational risk, and development of
common tools. The tools in this stage usually include selfassessment and risk process mapping. In addition, early indicators
of operational risk levels and collection of loss events are beginning
to be developed. These provide a common framework for risk
identification, definition of controls, and prioritization of issues and
mitigation programs. However, the most important factor in this
development stage is gaining senior management commitment and
ownership buy-in of operational risk at the business unit level.
Stage 3: monitoring. Once all of the operational risks are identified,
the need to understand the implications of these risks to the
business becomes pronounced. The focus becomes tracking the
current level of operational risk and the effectiveness of the
management functions. Risk indicators (both quantitative and
qualitative) and escalation criteria (which are goals or limits) are
established to monitor and report performance. Measures are
consolidated into an operational risk scorecard along with other
relevant issues for senior management. More banks have some
form of monitoring system for operational risk than have formal
operational risk measures. Most financial institutions monitor
operational performance measures such as volume, turnover,
settlement failures, delays, and errors. Some banks monitor
operational losses directly, with an analysis of each occurrence and
a description of the nature and causes of the loss provided to senior
managers or the board of directors. A consistent approach to
monitoring the operational performance measures and analyzing
them has not yet been agreed on because the various business
models are too different. Only a few banks have yet reached this
stage with their current information systems for capturing and
reporting operational risks.
Stage 4: quantification. With a better understanding of the current
situation, the need changes to focus on quantifying the relative
risks and predicting what will happen. More analytic tools, based
on actual data, are required to determine the financial impact of
operational risk on the organization and provide data to conduct
empirical analysis on causes and mitigants. The loss event
database, initiated in stage 2, now contains sufficient information
across businesses and risk types to provide insight into causes and
more predictive models. There may be a significant investment in
developing earnings and capital models, and establishment of a
new committee to evaluate the results.
Stage 5: integration. Recognizing the value of lessons learned by
each business unit (earnings volatility) and the complementary
nature of the individual tools, management focuses on integrating
and implementing processes and solutions. Balancing business and
corporate values, qualitative versus quantitative analysis, and
different levels of management needs, risk quantification is now
fully integrated into the economic capital processes and linked to
compensation. Quantification is also applied to make better
cost/earnings decisions on investments and insurance programs.
However, this integration goes beyond processes and tools. In most
leading companies, operational risk management is being linked to
the strategic planning process and quality initiative. When this
linkage is established, the relationship between operational risk
management and shareholder value is more directly understood.
Most banks considering measuring operational risk are at a very early
stage, with only a few having formal measurement systems and several
others actively considering how to measure operational risk. The existing
methodologies are relatively simple and experimental, although a few
banks seem to have made considerable progress in developing more advanced techniques for allocating capital with regard to operational risk.
The experimental quality of existing operational risk measures reflects
several issues. The risk factors usually identified by banks are typically
measures of internal performance, such as internal audit ratings, volume,
turnover, error rates, and income volatility, rather than external factors
such as market price movements or a change in a borrower’s condition.
Uncertainty about which factors are important is due to the absence of a
direct relationship between the risk factors usually identified and the size
and frequency of losses. This contrasts with market risk, where changes in
prices have an easily computed impact on the value of the bank’s trading
portfolio, and perhaps with credit risk, where changes in the borrower’s
credit quality are often associated with changes in the interest rate spread
of the borrower’s obligations over a risk-free rate. To date, there is little research correlating those operational risk factors with operational losses.
Capturing operational loss experience also raises measurement
questions. A few banks noted that the costs of investigating and correcting
the problems underlying a loss event were significant, and in many cases
exceeded the direct costs of the operational losses. Several banks sug-
Operational Risk
gested creating two broad categories of operational losses. Frequent,
smaller operational losses such as those caused by occasional human errors are viewed as common in many businesses. Major operational risk
losses were seen to have low probabilities but a large impact perhaps exceeding those of market or credit risks. Banks varied widely in their willingness to discuss their operational loss experience, with only a handful
acknowledging the larger losses.
Measuring operational risk requires estimating both the probability
of an operational loss event and the potential size of the loss. Most approaches described in the interviews rely to some extent on risk factors
that provide some indication of the likelihood of an operational loss event
occurring. The risk factors are generally quantitative but may be qualitative and subjective assessments translated into scores (such as an audit assessment). The set of risk factors often used includes variables that
measure risk in each business unit, such as grades from qualitative assessments including internal audit ratings; generic operational data such as
volume, turnover, and complexity; and data on quality of operations such
as error rate or measures of business riskiness such as revenue volatility.
Banks incorporating risk factors into their measurement approach can use
them to identify businesses with higher operational risk.
Ideally, the risk factors could be related to historical loss experience
to create a comprehensive measurement methodology. Some institutions
have started collecting data on their historical loss experience. Since few
firms experience many large operational losses in any case, estimating a
historical loss distribution requires data from many firms, especially if the
low-probability, large-cost events are to be captured. Another issue that
arises is whether data from several banks or firms comes from the same
distribution. Some institutions have started building up proprietary databases of external loss experiences. Banks may choose different analytical
or judgmental techniques to arrive at an overall operational risk level for
the firm. Banks appear to be taking an interest in how some insurance
risks are measured as possible models for operational risk measures.
As with market risk and credit risk, institutions are continually designing,
constructing, and improving operational risk management processes.
Many approaches currently exist, and every consulting company claims to
own the best practice standards. However, consulting organizations consistently assign operational risk responsibility to the management of the
operational business units of a financial institution. In general, business
units have been left to their own devices to build the appropriate infrastructure to manage their operations and the resultant risk. The challenge
is the extent to which an organization builds centralized operational risk
management processes to support this.
In order to create a consensus, it is most useful to consider the essential components of any effective risk management framework. A process
has to be established and maintained to enable management and the
board of directors to systematically:
Identify operational risks
Measure the extent of the identified operational risks
Monitor the nature and extent of operational risk
Control, within acceptable parameters, the operational risk
exposure of the organization
The essential elements of that framework should include:
The establishment of consistent standards for the identification of
operational risk, including the development of definitions and
terminology, from which the consolidated operational risk
exposure can be generated.
The establishment of reporting infrastructure to support the
independent monitoring and control of operational risk. Effective
organizational risk management requires independence between
the management of operational risk, resident within the operational
units, and oversight over the control of operational risk.
The development of consistent measurement methodology to
allow for consolidated analysis of the extent of operational risk.
Furthermore, from this measurement base, decisions can be
formulated on alternative risk transfer solutions, capital
management and control, and the implementation of riskadjusted performance measures.
There seem to be two distinct operational risk management approaches
being adopted across the financial services sector—a top-down and a bottom-up framework. However, even within these commonly used terms
there is a range of interpretations. Some organizations understand bottomup and top-down as the process through which the risks of the organization
are identified, while others use the terms to describe the nature of the measurement process that supports the operational risk management framework.
The conceptual differences between the approaches can best be characterized by the way risk is identified, measured, and aggregated within
the organization:
Operational Risk
Top-down approaches focus primarily on the view of risk within
the organization generated from the top of the organization. Risk
is identified, measured, and aggregated according to a
preexisting structure decided on and agreed on by top
management. As a result, a top-down approach tends to focus on
known or identifiable operational risk loss events. The impact
and likelihood of operational risks are generally determined by
reference to a combination of known external events and internal
views on relative exposures.
Bottom-up approaches focus primarily on the origins of risk
within the organization. Rather than focusing on views of risk
after the fact, bottom-up approaches focus on originating factors
(either internally or externally generated) to determine the
likelihood and impact of operational risk. Organizations are
generally managed through a combination of people, processes,
and technologies that either implicitly or explicitly manage risk.
Bottom-up approaches focus on the interaction between internal
and external events and the people, processes, and technologies
deployed throughout the organization. These points of
interaction provide the basis for identifying and determining the
likelihood and impact of operational risk.
The BIS approaches to operational risk can be compared with the
bottom-up and top-down approaches: the basic approach is a top-down
approach, and the internal approach is a bottom-up approach, whereas
the standardized approach is a top-down framework with bottom-up constituents.5
Top-Down Approaches
The unique aspects of a top-down approach to operational risk are generally found in the identification, measurement, and monitoring of operational risk (see Figure 4-5). Risk Identification
Risk identification in a top-down approach is driven by management belief that the organization is exposed to either direct or indirect loss. These
loss events are normally aggregated into risk categories that are consistent
with the organization’s definition of risk (see Figure 4-5). For example,
losses associated with the failure of technology would ordinarily be aggregated as technology risk.
The process of risk identification is ordinarily undertaken on either a
centralized or decentralized basis through a combination of a prepopulated database of loss events, fed from either internal or external sources,
F I G U R E 4-5
Top-Down Risk Identification and Aggregation.
Σ errors
Σ errors
Settlement and
confirmation reconciliation
Unknown security/product
Late delivery
Wrong delivery
Reconciliation error
Compliance error
Communication failure
Late confirmation
Settlement error
Counterparty error
Misplaced deal
Unconfirmed deal
Duplicated deal
Unauthorized deal
Wrong price
Limit control breakdown
Documentation error
Σ errors
Σ errors
Σ errors
and traditional risk discovery techniques such as risk workshops and control and risk self-assessment in the form of checklist, questionnaire, or prepopulated automated tools.6 Quite often organizations claim to have
implemented a bottom-up approach because the identification and measurement of risk are undertaken on a decentralized basis, i.e., within the
operational units. However, although the risks are identified from the bottom up, that identification and the resultant estimates of the likelihood of
occurrence and impact are based on separation and aggregation of risk
rather than origins of risk. In essence this would make these top-down approaches.
One key feature of top-down approaches is that they are most frequently established at a central point within the organization, such as the
risk management team. As a result, risks can be readily aggregated to facilitate central analysis. This aggregation can then be used to support the
measurement, management, monitoring, and control of operational risk. Quantitative Risk Measurement
A variety of approaches are used to support the top-down measurement
of operational risk. These approaches generally fall within two broad cat-
Operational Risk
egories: quantitative measurement using mathematical approaches to
quantify the level of risk, and qualitative measurement using more subjective assessment of risk (see Figure 4-6).
Operational risk in the context of quantitative risk measurement is
the volatility of earnings that can be measured in the course of carrying on
business, excluding the financial risks from market and credit risk.
Business risk in the context of quantitative risk measurement is the
risk of operational earnings volatility due to changes in the earnings mix,
margin, and volume volatility, and the level of variable and fixed costs.
Event risk in the context of quantitative risk measurement is the risk
of financial loss due to operational processes and activities. Event risks
such as earthquakes and terror attacks require special precautions. These
include the costs of contingency plans for postdisaster recovery, system
security, safeguarding of assets, and adherence to regulatory and legal requirements to maintain a minimum level of protection against event risks.
Business risk and market risk are two key types of risk that can affect
a company’s ability to achieve earnings or cash flow targets. While the relative magnitude of business risk and market risk varies across different
organizations, the concept is the same for all with different exposures to
different risks.
Business risk is defined as “the uncertainty of future financial results
related to business decisions that organizations make and to the business
environment in which organizations operate.” For example, business risk
can arise from strategy and investment decisions, marketing strategies,
F I G U R E 4-6
Event risk
Relationship of Frequency Versus Impact and Business Versus Event Risk.
Event risk
Operational risk
Business risk
product development choices, competitive differentiation strategies, pricing decisions, and sales volume uncertainty. These are the decisions that
contain inherent long-term conceptual risks that the management and
shareholders of organizations are expected to take in order to generate profits and to be compensated for the risks taken. However, market risk refers to
the uncertainty of future financial results arising from market rate changes
(equities, fixed income, foreign exchange rates, etc.). Market risk can affect
and expose an organization’s business in a variety of ways. For example,
operating margins can be eroded because of rising commodity prices or because of depreciating currencies for countries in which a company has foreign sales and thus cash flows in foreign currencies (direct market risk
impact). Also, changes in market rates due to price competitiveness can potentially force an organization to adjust the prices of its products or services.
In turn, this can affect sales volumes or competitive position depending on
the positioning, market share, and market exposures of the company and its
competitors (indirect impact of market risk on business profits).
Three of the more common top-down quantitative approaches focus
on earnings volatility, the capital asset pricing model, and parametric
methods for quantifying risk. Each of these methods is outlined in more
detail in the following sections. Earnings Volatility Approaches
Earnings volatility approaches are based on the assumption that volatility
in earnings, business cash flows, asset values, interest, or commercial margins reflects the risk of the firm. Accordingly, if the volatility can be attributed to operational events rather than financial risks (market and credit
risk), then this can be used to represent the operational risk of the firm. Institutions applying the earnings volatility approach will generally consider earnings volatility from a strategic and an event-driven basis.
When applying the earnings volatility approach, an institution
needs to consider the source of information to support the estimate of
earnings volatility and any other events to which the institution is exposed. In addition, earnings volatility may arise from nonoperational
sources, and therefore these sources need to be excluded to ensure that
only volatility from operational risk is being modeled. Before quantifying
the operational risk, the data required to model the loss events and the
volatility of income has to be run through a series of steps, as explained in
the following sections.
Obtain Earnings Series
One possible source of earnings volatility can be discovered through the
analysis of historical earnings. If the institution is prepared to accept the
assumption that the historical earnings stream is an appropriate proxy for
future earnings, this can form the input basis of the measurement process.
Operational Risk
Accounting earnings are generally an easy source for historical earnings. This approach may be enhanced through budget data or other earning forecasts to extend the loss prediction into the future. The length of
time over which the time series should be collected will vary from institution to institution, but should be long enough to support statistical evidence. A key element in collecting data is to ensure general consistency in
the nature of the raw data. In some instances it will be impossible to generate consistently formed earnings streams, e.g., as a result of restructuring, takeover or merger, or significant changes in activities or divestments,
etc. Additional attention is required to determine whether volatility in
earnings streams is a result of changes in accounting policies.
Eliminate Volatility from Market and Credit Risk
A certain portion of the historical earnings volatility can be contributed to
market and credit risk. An organization with an effective funds transfer
pricing mechanism to account for earnings will be able to provide a reasonable proxy to separately identify volatility in earnings associated with
nontraded market risk, whether related to interest or exchange rates.
The degree to which volatility in earnings contributes to credit risk
can be difficult to assess, although there are generally clearly identifiable
elements of earnings associated with the credit loss and provisioning
process under existing accounting and regulative rules such as U.S. generally accepted accounting principles (GAAP) or international accounting standards (IAS). However, the impact from changes in the credit
spread will not be identified separately from other impacts, such as market risks. Most accounting earnings series are set up on the basis of historical cost, and therefore any volatility associated with credit margin
changes will be absorbed (and thus averaged) in the overall earnings
Careful analysis of the earnings series is required to avoid doublecounting volatility arising from credit and market risk when combining
market value at risk, credit value at risk, and net interest earnings at risk.
Eliminate Funding of Shareholder Equity
The cost of shareholder equity should be excluded from the accounting
earnings series so that the mean of the series is appropriately calculated
based on the underlying business and not the financing structure of the
underlying organization.
Calculate Mean and Standard Deviation
The mean and standard deviation of the earnings series can be used as a
starting point for the calculation of capital required to withstand the
volatility of earnings as a result of operational risks. The critical assumption to be defined at this point is what is the appropriate confidence level
on which to base the understanding of volatility from mean earnings. The
first approach may be to select a confidence level consistent with the current credit rating of the organization.
Identify and Model Fat Tail Events
In the analysis of the earnings series, it is highly probable that the structural changes in earnings will impact the series generated from changes in
market-related factors or from one-off events such as major operational
failure changes in accounting rules, tax regulations, etc. Careful consideration needs to be given to whether these impacts should be separately
identified or modeled.
Historical earning time series will generally involve losses associated with operational and process problems, but will not necessarily reflect all events that the organization may be potentially exposed to. As a
result, separate consideration will need to be given to nonrelated one-off
events that could occur. This can be taken into account through the estimation of the likelihood of impact and frequency determined during the
risk identification and measurement process using filtering techniques
(see Figure 4-7). Alternatively, external loss databases can be used to support the estimation of potential impacts and frequencies.
F I G U R E 4-7
Frequency/likelihood of loss
Distribution and Modeling of Fat Tails.
Expected loss
Unexpected loss
Catastrophic loss
99% (or higher)
Impact/magnitude of loss
Operational Risk
Combine the Impact of Separately Identifiable
Loss Events and Volatility of Income
The outcomes of the two approaches need to be integrated to provide an
estimate of the total measure of operational risk. There are a number of
ways this integration can be undertaken, ranging from simple additive
statistical techniques to the use of historical or Monte Carlo simulation. Capital Asset Pricing Model Approaches
Several approaches based on financial market theories can be applied to
the measurement of operational risk, such as the capital asset pricing
model (CAPM). The CAPM claims that an investor should receive excess
returns in compensation for any risk that is correlated to the risk in the return from the market as a whole. However, the investor should not receive
excess returns for other risks. Risks that are correlated with return from
the market are referred to as systematic. The remaining risks are referred to
as nonsystematic or endogenous. The structure underlying the CAPM for an
organization can be expressed as follows:
rfirm = rrisk free + βfirm ⋅ [rmarket − rrisk free]
The CAPM assumes that the risk of an individual position is well
represented by its beta (β) coefficient. In statistical terms, the beta coefficient is defined as the covariance of the return of an individual position
against the market portfolio return (or another benchmark) divided by the
variance of the market’s return. Companies with a beta of 1 tend to behave
in direct proportion to the market; companies with a beta of less than 1
move in relative terms less than the market and, conversely, those with a
beta of more than 1 move faster than the market.
The capital required by an organization is a function of the required
return of the organization:
required earnings
equity at risk = ᎏᎏᎏ
Equity is the equivalent amount of capital that is required to generate the required earnings given the risk-adjusted rate as determined under
the CAPM. In order to convert the required rate of return into a numeric
figure, the CAPM concept is applied to the market value of the firm,
which drives the calculation of beta.
There are limitations in using the CAPM to measure equity requirements for operational risk:
The beta concept is assumed to be fully leveraged in that is it is
derived from market observations of returns from firms that use
a combination of debt and equity to fund their financial needs.
Leverage can be defined as being composed of financial leverage
(the extent to which the institution relies on debt to generate
revenue) and operating leverage (the extent to which the
institution relies on fixed costs in the generation of revenue). In
order to obtain a true measure of the capital requirements for
operational risk, the effects of financial and operational leverage
need to be separately identified.
The beta concept is based on historical time series, and any
change, such as in organizational structure, market structure, tax
laws, etc., will only be adequately reflected in the beta measure
after a certain amount of time has passed.
Applying the Approach in Practice
Measurement of the stock market beta is relatively transparent for listed
companies, but becomes less transparent for unlisted companies. In practice this is overcome through a proxy process that assumes there are
listed companies that can be considered peers for unlisted companies
with similar country exposures, industry position, size, and organizational processes.
CAPM-based approaches can be difficult to apply without detailed
knowledge of profit/loss accounting practices, tax considerations, etc.
The calculation of operating leverage is difficult, as the organization has to
maintain a consistent split between fixed and variable costs over time.
There is no unique industry standard for the treatment of costs across industries and between the different national accounting structures. Parametric Measurement
Parametric measurement has gained ready acceptance in the quantification of financial risk. Not surprisingly, concepts such as parametric value
at risk (VaR) and similar simulation-based techniques are being frequently
implemented to support the measurement of operational risk. Generally,
these methods are similar to those being used for the modeling of one-off
events in both the earnings volatility and CAPM measurement approaches.
Parametric approaches primarily focus on the ex post facto analysis
of historical loss data to support the calculation of a loss distribution. The
loss probability distribution can be either broken down into specific loss
events or categories of risk or figured for the firm as a whole given the aggregation of all potential loss events. The loss probability distribution can
be applied to the measurement of expected losses (forecasting), using the
mean of the distribution, or of unexpected losses, using the standard deviation of the distribution.
Operational Risk
Applying the Approach in Practice
Applying the parametric approach in practice has proven difficult due to
the lack of historical loss data within most organizations. Collecting data
has proven to be quite imperfect, requiring the application of extensive
data collection techniques. In some instances, the absence of internal data
has been addressed through the application of external loss databases.
These loss databases provide proxy loss probability distributions that can
be applied to support internal information sources.
While the parametric approach is a valid measurement alternative
for most operational losses that have well-defined distributional characteristics, there are some loss events that create a statistical challenge. These
losses, characterized by low frequency and high impact, require the introduction of alternative statistical methodologies, such as extreme value
theory, to complete the full measurement framework. Based on historical
experience, it is generally these events that are the most difficult to capture
statistically and that lead to large numerical operational loss. Qualitative Risk Measurement
As a result of the difficulties experienced in the quantitative measurement
of operational risk, and given the fact that there has always been operational risk across and within organizations, there are a multitude of qualitative risk measurement approaches that have been employed. These
approaches, while fundamental to support the management of operational risk, generally provide judgmental or relative rather than absolute
measures of operational risk.
When applied in a top-down approach, qualitative measures tend to
focus on the assessment of risk within the organization. Using techniques
outlined in the preceding risk identification sections, organizations generally define a series of indicators that provide the basis for assessing
whether the impressions of risk change over time. These indicators are
often characterized according to what they indicate. Key Performance Indicators (KPIs)
KPIs are simply tracked events that raise red flags if they go outside an established range. As the name suggests, KPIs are ordinarily associated with
the monitoring of operational efficiency. Examples of KPIs include failed
trades, customer complaints, staff turnover, transaction turnover, systems
downtime, and transaction throughput.7 Key Control Indicators (KCIs)
KCIs are indicators that demonstrate the effectiveness of controls: for example, the number of items outstanding on a nostro reconciliation, the
number of outstanding confirmations or unconfirmed trades, the number
of fraudulent checks, etc.8
314 Key Risk Indicators (KRIs)
KRIs build on the concepts of KPIs and KCIs to construct leading indicators. By combining performance indicators and control indicators, such as
staff turnover and transaction volume, an indicator can be created that allows insight about the stress that core processes will be facing. Rather than
being considered new indicators, KRIs are a different means to combine
traditional measures.9
Qualitative risk measures are generally built into the risk monitoring
and control process in a manner consistent with the identification of risk.
Bottom-Up Approaches
Bottom-up approaches are characterized by the identification, measurement, and management of the causes of operational risk within the organization, rather than focusing on losses that are symptoms (outcomes) of
operational failure. Risk Identification
Bottom-up approaches focus primarily on the identification of the potential sources or causes of loss within the organization. These are generally
driven by the interaction and reaction of the employees, processes, and
technology of the institution combining both internal and external
events. The sources of operational risk are generally not the result of a
simple linear cause-and-effect relationship. Operational risks are viewed,
rather, as a result of an entangled web of both internal and external influencing factors.
The process perspective is critical in the identification of risk because
of the tendency for risks and losses to be transferred from one part of a
process downstream. For example, if a reconciliation/after-trade compliance check is not performed in a timely manner, an investment decision
might be based on unreconciled and thus (potentially) misleading information.
It follows that the basis for identifying operational risk in a bottomup environment is to break the organization down into its core
processes—those that are aligned with the achievement of the organization’s strategic objectives and responsibilities (see Figure 4-8). Each core
process can generally be broken down into a series of subprocesses. While
this may appear to be a sisyphean task for a large and complex organization, it would probably not be necessary to extract all of the processes of
the organization. It is likely that the majority of the organization’s operational risks will result from a few critical processes and a relatively small
number of possible loss events.
For each of the critical processes and subprocesses, an analysis is
performed to determine the risk exposures, or potential risk exposures,
Operational Risk
F I G U R E 4-8
Bottom-Up Risk Identification and Aggregation.
Regulatory capital
Unsupportable deal
Late delivery
Breakdown of regulatory
required supervision
Late confirmation
Unauthorized deal
Settlement error
Limit control
Market exposure
Communication failure
Short exposure
and the potential downside events that could result in the inability of the
organization to meet its strategic objectives (and thus in losses). These risk
exposures or potential weak processes have an inherent causal structure
that needs to be identified and monitored to provide the appropriate inputs for the measurement and reporting of potential operational risk exposures.
For most loss-generating events there is usually a chain and a hierarchy of events that influence either the size or occurrence of a given event.
These combinations/sequences are normally described as “and/or”
events. Through the analysis of the hierarchies of events, a tree of causes
can be constructed.
CHAPTER 4 Quantitative Risk Measurement
There is a range of flexibility in the methodologies for modeling operational risk from the bottom up. These methodologies differ significantly.
Therefore, the following sections cover the two main alternatives.
Agent-Based Simulation
One alternative is to measure the impact of operational risk through the
application of complexity and simulation theory. The analysis of complexity is an interdisciplinary science that attempts to uncover the underlying
principles governing complex systems and the emergent properties they
exhibit. Such systems are composed of numerous simultaneous and varied interacting components.
In complex systems, sophisticated and unpredictable properties
arise from an interacting group of agents. Examples of such emergent
properties include how the system organizes itself, how it finds a balance
between order and disorder, and how agents evolve new behaviors in response to change. Examples of emergent properties in business applications include the volatility of security prices, the speed with which supply
chains can reconfigure themselves in response to changing market requirements, and the dominance of one technological alternative over another, such as a technological advantage.
Using the simulation capabilities afforded by computers, visionary
biologists, mathematicians, physicists, and computer scientists have observed the emergent properties of complex adaptive systems in action.
Models of artificial systems can be developed that run many different scenarios, and the resulting emergent properties can be analyzed without any
risk to the system.
Agent-based modeling techniques can be used to study complex
adaptive systems such as manufacturing plants, corporations, industries,
markets, and sectors of the economy. In agent-based modeling, systems
are modeled as clusters of autonomous decision-making entities called
agents. These agents individually assess their situation and make decisions based on a set of rules. At the simplest level, an agent-based model
consists of a cluster of agents and connections between these agents.
Agents may execute various behaviors such as selling, buying, storing, reporting, etc. Compared to traditional modeling techniques, this distributed decision-making process does not result in a system of fixed
equations that can be solved mathematically. However, by including
repetitive, competitive interactions between agents using simulation techniques, it allows for a much more realistic estimation and presentation of
a system because it emulates the manner in which the real world operates.
Applying an agent-based simulation approach requires the combination of a comprehensive understanding of the processes and operational
characteristics of an organization and a detailed understanding of modeling
Operational Risk
techniques using complexity theory. The first step in applying an agentbased simulation to support the measurement of operational risk is the construction of a model of the business processes. This model is similar in
principle to a traditional process decomposition of the organization. Each
process within a business entity covers the interaction of people, technology, and generally observable events. The observed business process can be
described by schematic figures or equations, and individual behaviors can
be mapped by sets of if-then rules. The business model is translated into a
computational description for the simulation environment.
A simulation environment is used to run multiple simulations of
both the qualitative and quantitative dimensions of the model to determine loss probability distributions. Running the simulation enables calibration of the model with existing data and operational knowledge by
comparing backtesting data with the realized data. Once it becomes apparent that the model is operating on a basis consistent with reality, it can
be applied to support traditional techniques such as value at risk and
stress testing to obtain robust risk measures.
Causal Modeling
Models that can be used in a bottom-up approach build from the causal
tree as discussed earlier. These models range in practice from true internal
causal models to hybrid models that combine external and internal data
and simulation techniques to determine loss probability distributions. The
loss probability distributions from either modeling approach can be used
to generate estimates of expected and unexpected losses, which are traditional measures of risk.
Causal modeling uses the concept of conditional independence to
generate joint probability distributions for all loss events. These distributions are used as a basis for calculating ranges of potential loss. Actual
data is used to drive the generation of probability distributions. The absence of accurate and relevant historical data is one of the potential problems with the implementation of causal modeling. However, this can be
overcome by combining internal data with external loss databases.
The events in a loss probability distribution have two attributes: frequency and impact. A bottom-up approach allows for the generation of
separate distributions of both frequency and impact. From a risk management point of view, this allows for the separate analysis of the applications
of controls and alternative risk transfer, and provides a financial incentive
to assign personnel to reduce either the frequency or impact of loss (see
Figures 4-9 and 4-10).
Data for frequency distributions can come from a variety of sources,
including insurance data, external databases, management information
systems, loss event analysis reports from expert groups, etc. The most obvious approach in developing a frequency distribution is to maintain a
F I G U R E 4-9
Distribution of Operational Risk Events Under Equal Probability Assumption.
Time periods between loss events
register of time-stamped loss events. A distribution can be fitted to this
raw data and can serve as the basis for modeling probability. In the absence of actual data, a simulation tool could be used in combination with
a subjective estimation of the parameters of that distribution, such as time
horizon, standard deviation, confidence interval, distribution profile, etc.
The empirical data for generating and fitting impact distributions
can come from a variety of sources depending on the nature of the events
F I G U R E 4-10
Distribution of Operational Risk Events Under Unequal Probability Assumption.
Impact of loss events
Lowest Mean
Operational Risk
identified in the causal analysis. However, if there is insufficient historical
data or statistical evidence from the existing historical data to support the
generation of an appropriate probability distribution, simulation models
can again be used to drive the generation of a distribution.
Combining the outcome of the separate estimation of frequency and
impact in another simulation will provide a distribution of loss events.
From the loss distribution, the expected loss (mean of the loss distribution) and the unexpected loss (the standard deviation of the loss distribution) can be calculated. The core limitation of using simulation in this way
is the use of fixed conditional probabilities to create the causal tree. In a
causal model, the conditional probabilities are not stationary, and application of a bayesian approach can be updated continuously. Qualitative Risk Measurement
Bottom-up qualitative measures generally incorporate indicators that are
found in the top-down approach. The critical difference is the extent of
linkage with the causes of loss rather than the overall impressions of the
indicators of the loss itself. This important difference is given from the
basis of risk identification undertaken.
In a bottom-up approach, it is possible to focus on indicators that are
meaningful for effective risk management and control, because the approach is driven from within the organization through the interaction of
people, processes, and technologies with internal and external events. In
general, these indicators will be largely consistent with those used on a
daily basis by operational line management.
Organizations have realized that tracking too many KPIs can become overwhelming and confusing and, thus, ineffective. An efficient organization will need to decide and focus on which indicators are tracked
continuously and which are sufficiently static to be tracked on a less dynamic basis.
4.9.3 Top-Down Versus Bottom-Up Approaches
Whether one approach or the other is more appropriate depends on the
circumstances of each organization and that organization’s view on the
balance between the drivers for establishing operational risk management
frameworks. There is no right answer to whether a top-down or bottomup approach to operational risk is best. The discussion is ongoing as to the
feasibility, accuracy, and value of quantifying operational risk. The soft
and variable nature of many operational risk elements supports the skeptics’ argument that it is just not possible to accurately quantify operational
risk and that therefore there is little value to be derived from even attempting to do so. And, it is true that the range of factors underlying and
influencing operational losses is so diverse that it makes finding a com-
mon basis on which to provide a measurement framework challenging.
The fact remains that the ultimate organizational goal of measuring performance of the entire organization, on the basis of a fully risk-adjusted return on capital, will never be achieved without including a reasonable
value for operational risk.
It may never be possible to model, and thereby quantify, all possible
events of operational risk. The only data that will ever be available to use
in modeling will be based on the frequencies and impacts of failure scenarios that occurred at some time in the past. Similarly, all VaR-based simulation is inherently flawed owing to the fact that what happens in the
future is not necessarily related to the past. However, all simulation-based
risk quantification models, including the assumed and proven market and
credit risk modeling approaches, will be limited by these general assumptions. Despite these inherent limitations, there will always be value and
benefit in risk management if there is a consistent basis for measurement
such that management, the board of directors, and the shareholders have
a clear understanding of their risk position and a reporting process that
enables them to rank risks.
It should be clearly recognized that there are certain categories of operational risk events at the extreme ends of the risk spectrum for which it
can be argued that modeling is irrelevant. For example, why try to model
the likes of a major reputational failure scenario for the purpose of capital
allocation, or a major loss such as in the Barings case, when it is more
probable that should such an extreme event actually occur, it would wipe
out the organization’s capital base anyway? What is certain is that it will
never be possible to get to the quantification end game without first developing the framework.
It is becoming increasingly obvious in the financial services sector
that one or the other approach is not necessarily sufficient and that, although a specific method of capital allocation is useful, existing methods
may not only be inaccurate but may be counterproductive and misleading
for comprehensive operational risk management. Taking a purely topdown approach can limit an organization’s ability to understand the practical risk drivers and may therefore restrict the management and
mitigation function. Taking a purely bottom-up approach may result in a
granular, low-level focus that might not contribute to achieving strategic
objectives. More than likely the answer is to combine the two approaches.
4.9.4 The Emerging Operational Risk Discussion
Over the past months and years, the banking industry has entered into intensive discussion over capital requirements for operational risk. It seems
that some institutions have come to initial conclusions in their strategic
thinking about operational risk; what it means to their organization; and
Operational Risk
how they could go about quantifying it in a way that suits their strategic
objectives, culture, and processes. Diverse approaches have evolved over
a short period of time and/or have been adopted from other disciplines.
Some approaches have resulted in top-down orientations and the attendant risk of overemphasis on capital management as opposed to risk management. Other organizations have done the reverse by starting with a
nuclear look at business processes at the lowest operational level to discover where their operational risks might lie, then subsequently integrating and aggregating these risks into a quantification process.
To a certain extent, the pace of this evolution has been supported by
an insatiable industry desire to understand and develop risk management
concepts, terminology, and tools. In today’s margin squeezing environments, where any potential marketing angle or competitive advantage is
zealously guarded, operational risk management is perceived as another
way to better allocate and use economic capital. The need for information
and the problematic process associated with setting up an operational risk
framework requires industry responses. Formal and informal discussions
in academia and the financial services have increased and intensified and,
to a certain degree, there is a need to intellectually stress-test them. These
developments, together with structured research, have been responsible
for some of the standard terminology that evolves in tandem with distinct
methodology approaches to risk management.
Operational risk and regulatory capital have existed in separate spheres
for some time. However, most formal papers that have been issued by regulatory bodies have merely committed to the intent to a capital adequacy
structure for operational risk as a separate risk class. The Basel Committee, although not a supervisory body, has been providing the industry
with regulatory best-practice guidelines and standards since 1975. It has
been paving the way for an additional risk class to be implemented into
the supervisory framework. For example, Principle 13 of the 1997 Basel
core principles for effective banking supervision says:
Banking supervisors must be satisfied that banks have in place a comprehensive risk management process (including appropriate board and senior
management oversight) to identify, measure, monitor and control all other
material risks and, where appropriate, to hold capital against these risks.10
Local regulators will be the ones to adopt and implement the Basel
Committee’s outline and be responsible for the day-to-day monitoring
and enforcement of any regulatory capital charge. There is currently a
tremendous amount of attention from local authorities on the industry
discussion papers. Some local regulators will undoubtedly be more active
than others. For example:
In the United States, representatives of the Federal Reserve are
cochairing the risk management subgroup of the Basel
Committee. The topic of operational risk management is raised in
virtually all U.S. bank examinations today, but the Fed and the
Office of the Comptroller of the Currency (OCC) view
operational risk from different sets of risk classes.
In the United Kingdom, the Financial Services Authority (FSA) is
a relatively new body and is undergoing incremental change in
terms of its scope and powers. The FSA has been keen to immerse
itself in the undercurrent of activity regarding operational risk
evolution and has tried to draw from all spheres of expertise on
the topic.11
In Germany, the national regulator is following developments
closely, but some representatives have expressed concerns over
enforcement powers and the fact that there has not been adequate
time for best practices to emerge.
In Japan, regulators have already begun to implement a boxscoring approach to bank risk profiling. Meanwhile a 25 percent
assessment of expense is already made on securities firms. From a
risk management incentive standpoint, such an approach is less
than optimal.12
In Australia, the Australian Prudential Regulatory Authority
(APRA) expects to follow the lead provided by overseas
regulators, after careful local analysis, with discussion papers and
policy statements in relation to operational risk capital.
In Switzerland, the national regulator actively participates in the
working committee of the Basel Committee and will adopt and
enforce the recommendations rigorously, given the involvement
of the Union Bank of Switzerland (UBS) in the LTCM debacle.13
Meanwhile, regulators in most countries agree that progress by
banks is required. Some regulators already require an operational risk
management function for domestic banks, e.g., the Saudi Arabian Monetary Authority (SAMA).
Following is a summary of comments reflecting the current regulatory discussions:
There is a consensus that, because of its unique characteristics, a
separate treatment of operational risk is appropriate.
No common view exists regarding additional capital for
operational risk. Critics of this approach suggest that a bank
Operational Risk
demonstrating sound risk controls and systems might succeed in
making a case for no additional capital. This would be enforced
by local regulators and monitored and reported by auditors.
Regarding additional capital requirements (beyond 8 percent),
apparently few if any institutions are willing to commit to the
notion that the industry is currently undercapitalized. Some
institutions have noted that it may not be possible to resolve the
“8 percent debate” until a common approach to credit risk capital
is settled on.
Practitioners express that the market risk guidelines have actually
freed up capital for some institutions, and thus it should be
possible to let overall capital percentages float above or below 8
Recently, opinions were voiced favoring integration of the market
and credit risk multiplier in one measure, given the difficulties of
segregating market and credit risks in some cases and the
potential to arbitrarily switch between regulatory regimes
depending on what is deemed better for the bank.
Any approach should support Pillar II regarding supervisory
objectives. The value of risk assessments, the use of risk
indicators, and control process assessments have all been
discussed. However, one consistent concern is that many selfassessment approaches are too granular to use in support of
modeling, especially given the fact the uniformity of such a
granular approach applied across various organizations with
different technologies, strategic objectives, etc. is not enforceable.
There are thousands of registered banks worldwide, each with its
own organizational structures, core competencies, and
specializations. And there is a wide variety of influences on any
particular institution. Regulators, consultants, vendors, and the
banks themselves have to operate in markets around the world
where there is a huge range of sophistication relating to the
idiosyncracies just listed.
There has not yet been a worldwide operational risk initiatives survey that adequately captures and reflects the relative progress of a wide
spectrum of banks relating to operational risk management efforts. Only
approximately 3 to 5 percent of the worldwide banking population is actively investing time and money in developing an operational risk framework. If we were to look at the aggregate asset or balance sheet size
represented by these groups, the percentage would definitely be much
higher. But if we examine the size and activity of the banks that have failed
or have sustained embarrassment or reputational damage, we see that op-
erational risks at smaller institutions—e.g., the Banco Ambrosiano fiasco—cannot be ignored.14
The British Bankers’ Association (BBA) set up an operational risk advisory
panel in 1998, comprising a diverse group of banks believed to have an active interest in operational risk management. One of the panel’s primary
objectives was to assist the BBA in lobbying regulators about the type of
frameworks that might work best for the industry as a whole, rather than
having a methodology imposed on the industry that contradicted industry practice.
Later in 1998, the BBA panel, the International Swap and Derivatives
Association (ISDA), and Robert Morris Associates (a U.S.-based industry
body with a membership of over 3000 financial institutions) surveyed the
financial services industry. The results of the survey, which were unveiled
in early November 1999, have helped to crystallize the industry consensus
on operational risk capital.15
The BBA lists several factors that it believes underlie the Basel proposals. These include:
A recommendation to provide incentives for sound operational
risk management.
A recommendation to capture within the capital framework
businesses that are, in regulatory capital terms, almost entirely
risk free, e.g., custody and fund management.
A perceived need for a balancing charge to redress an anticipated
drop in regulatory capital held for credit risk. This line of
thinking is also expressed in the argument that operational risk is
implicit in current regulatory capital levels.
There are probably at least five perspectives emerging in the financial services community today about what an individual organization can
accomplish with operational risk management, and how to accomplish
these goals by applying objectives related to capital risk management and
operational risk. These range in focus from risk management analytics
and risk measurement, to control group focus, to business line management teams, to firmwide multidisciplinary operational risk management
Risk measurement. This dimension is perceived as a key objective
driven by the recent urgings of banking regulators. Owing to the
breathless pursuit of analytical precision, the first perspective has
focused entirely on risk measurement, including finding a
Operational Risk
number or a series of numbers to represent the range of possible
outcomes and demonstrating how this can be used to reduce
potential losses or exploit opportunities in the market. This
primary focus on modeling is based on the belief that a number is
critical for emphasis, attention, and focus of purpose. The
greatest challenge for these people will be in proving not only
that they have achieved analytic precision, but also that these
measures may be used to improve behavior and lower the
downside or increase profits.
Internal controls. The second perspective represents the opposite
end of the spectrum—those who have practiced operational risk
management in the form of one or more control disciplines (e.g.,
internal auditing, control, compliance, etc.), whose focus has been
on maintaining tight controls or corporate risk management
structures. It is tempting, and in some cases conceivable, that a
move to the emerging discipline of operational risk management
is a small leap from their current role(s).
Business management. Business managers have managed their
businesses based on several measures, such as KPIs, management
accounting information, etc. They allocated the investable capital
based on all this information. For this group, the move to track
and analyze operational risk indicators is certainly not foreign,
and may only require a slight refocusing supported by additional
firmwide information available to them.
Insurance risk management. This dimension is becoming more
visible in the operational risk management discussion, as
evidenced by the desire among firms for more effective operational
risk hedges versus less relevant traditional insurance coverage.
Multidisciplinary operational risk management. This emerging
function is perceived as the most effective operational risk
management program, which will incorporate the most effective
features of all four previously mentioned schools of thought:
(1) using quantitative and qualitative risk measurement tools
for estimating the dimensions of the operational risk exposures;
(2) applying the most effective risk management and risk control
tools; (3) monitoring risk drivers and indicators, similar to the
early warning indicators, through the use of management
information systems (MIS) tools with the objective of creating
a comprehensive operational risk management program;
(4) applying well-known risk finance and insurance tools as
operational risk hedges. Taken together, information from all of
these efforts contributes to what we have begun to refer to as a
firm’s operational risk profile.
These practical risk management perspectives contrast with the regulatory objectives, known as the three pillars, which include minimum
capital requirements, supervisory review, and effective use of market discipline. Regulators are seeking a strong but competitive banking system.
The defining issues are when and how risk capital will be viewed alongside these objectives. A significant amount of banks note attempts to allocate economic capital to operational risk, but reportedly nearly all are
dissatisfied with both their own methodology and the behavioral incentives created. Few if any use measures of operational risk capital to drive
business decision making or behavior. There is widespread concern that
any regulatory initiative in this area may retard or misdirect what have
been very positive initial industry efforts to date.
Overall, the industry response to the proposal has been negative and
a constant series of concerns has been articulated:
Definition. It is difficult to conceive of how to develop a risk
measure without a clearly defined risk boundary. No positive
industry standard currently exists.
No additional capital. The banking industry does not believe that
regulatory capital to support operational risks in excess of current
levels is justifiable. In the context of the opening Basel proposals,
it is difficult to see how there would not be an additional charge
for the majority of banks.
Duplication. How will overlap between the various risk
assessment processes (market risk, credit risk, operational risk,
and supervisory review) be managed, and will the level at which
current variable factors are set (market risk multiplier, target/
trigger) be adjusted as a result? This would require modifying the
existing credit and market risk regulations, meaning another
lengthy process.
Level playing field. This issue is a substantial concern for all
banks. At an international level, there is concern that any
regulatory capital charge for operational risk identified may well
not be applied consistently—or at all—in some other
jurisdictions. At a national level, this is more an issue of ensuring
consistency of assessment and a positive bias toward better
operational risk management.
Behavioral incentives. The issue of developing positive behavioral
incentives is based on the development of a risk-sensitive
assessment methodology. All the available options have
considerable flaws. There is a real concern that perverse behavior
will be encouraged if the regulatory hurdles are blunt and high.
Banks are much more likely to concentrate on arbitrage or
Operational Risk
Changing business environment. In parallel with the development
of risk management practice, the business of banking is itself
undergoing a period of considerable change because of new
businesses, products/services, organizational models,
competitors, e-commerce, etc. This again supports the argument
for a flexible methodological approach.
Developing efforts. There is concern that the enforced
implementation of a prescriptive methodology will retard or
misdirect industry development efforts. There is also concern that
the short-term regulatory need to develop an assessment
methodology might obscure the pace of development. As a
consequence, any methodological solution should, from the
outset, be characterized as interim and open to replacement or
change as industry practice progresses. Equally, there is a
common opinion among many industry practitioners that a
misaligned interim standard may do just as much damage even
though it may be temporary.
4.11.1 Measurement Techniques
and Progress in the Industry Today
The term measurement in the operational risk context can encompass a
huge variety of concepts, tools, and information bases. It is virtually certain that the approaches might differ wildly. This could be one of the problems that regulators face even if they do stipulate a particular method, as
the interpretation and application may give rise to many variations on the
same theme. Perhaps the supervisors and the local regulators should actually rely on this happening.
The following sections summarize some of the more mainstream
methodologies and provide an overview of what supervisors have been
considering most recently. Practitioner Measurement Methodologies
Risk indicator or factor-based models are methodologies that originate
from risk indicator or loss information. These tend to give rise to bottomup approaches due to the granularity and nature of the source of information.
Usually, information is readily available.
If constructed properly, it is transparent to the management of the
business line.
Business line management tends to accept the outcomes.
Collection, filtering, and aggregation of consistent data across the
firm is challenging.
Capturing interdependencies or overlaps between areas is
difficult (and sometimes impossible).
Internal experience is required.
Forecasting general trends is possible, but not particular
predictive forecasts on a detailed level. Economic Pricing Models
These models incorporate forecasting based on financial data and application of modeling. Probably the best known in operational risk circles is the
capital asset pricing model (CAPM), which is based on the assumption
that operational risk is responsible for an institution’s stock price beta. It
assumes that operational risk is the differential between credit and market
risk and the security’s market value.
Usually, information is readily available.
If constructed properly, it is transparent to the management of the
business line.
Business line management tends to accept the outcomes.
Collection, filtering, and aggregation of consistent data across the
firm is challenging.
Capturing interdependencies or overlaps between areas is
difficult (and sometimes impossible).
Internal experience is required.
Forecasting general trends is possible, but not particular
predictive forecasts on a detailed level. Risk or Loss Scenario–Based Models
These models attempt to summarize possible operational risk/loss outcomes for a variety of scenarios that are often mapped into a matrix of
probabilities such as frequency and severity of outcome. Scenario models
are reliant on the vision, breadth of knowledge, and experience of the person(s) conducting the modeling.
Experience and expectation of business line management is
included in the process, and is well accepted.
Conceptual, intuitive, and easy to understand and implement.
Operational Risk
Can help to accentuate areas for improvement in business strategy.
Supports identifying and building a robust firmwide disaster
recovery plan.
Supports management in the development of a structured crisis
management approach.
Often based on personal experience or expertise and thus
subjective. (Individual perception has a high influence on
scenario development.)
It is difficult to implement an entire portfolio of scenarios that
are really a representation of the institution’s operational risk
exposure. Statistical/Actuarial Models
These are one of the more common modeling bases in banks today, although approaches differ. Commonly, the source information will be an
operational risk event and loss data, which can also be a mix of data internal and external to the institution. Frequency and severity distributions
are assembled based on the data and then simulated via a technique such
as Monte Carlo to arrive at a range of possible loss outcomes. Figures are
produced for a stipulated time horizon and range of confidence levels.
Forward-looking; ensures that users are aware of its predictive
By definition, based on empirical data and thus more defensible
than subjective scenarios. (See remarks regarding risk- or lossbased scenarios in Sec.
It is difficult and time intensive to ensure accurate and timely
data collection and filtering processes given the depth of
information required to calculate a firm’s operational risk capital.
In purely quantitative approaches, there is no qualitative
Without a motivational incentive element built into the
methodology, it is difficult to get buy-in from the business line. Hybrid Models
In the end, an optimal modeling approach has not yet been identified. Each
has its advantages and disadvantages. At Bankers Trust, the operational
RAROC framework and modeling process developed from 1992 to 1998
has been a combination, or hybrid, of several of the approaches outlined in
the preceding sections, attempting to represent the best features of each.
Some important lessons were learned about operational risk modeling and capital adequacy in the process. For instance, from design through
implementation we found ourselves having to battle the tendency of business line representatives to reduce their capital allocations as a prime objective, in contrast to, and at the expense of, more primary risk mitigation
objectives. But through a combination of model approaches, including a
statistical/actuarial and scenario-based measurement approach blended
with risk factor and issues-based methods, we were able to make far
greater headway toward satisfying the risk measurement objective and
the objective of providing incentives for productive risk management behavior.
4.11.2 Regulatory Framework for Operational Risk
Overview Under the New Capital Accord
In the 1998 accord, the Basel Committee made an implicit assumption that
“all other risks” were included under the capital buffer related to credit
In its new recommendations, the committee proposes rather more
accurate and complicated methods for calculating capital charges for
credit risks, and has for the first time attempted to deal with operational
risk as an entity in its own right.17
It is important to note that it is presently unclear whether all of the
national bank supervisors who implemented the original 1988 capital accord will require all of their regulated institutions to meet the proposed
BIS standards.
The mission for the banks that do eventually fall under the purview
of the Basel guidelines is to quantify operational risk in order to set aside
capital to cover future losses. The expectation is that around 20 percent of
all bank capital will be allocated to operational risk, but individual banks
may hold more or less than this proportion based on the sophistication of
their operational risk management. In the spirit of the preceding discussion, the discretionary element of regulation means that capital discounts
will only be given to banks that can demonstrate their ability to measure,
control, and manage operational risks.
The Basel Committee is recommending an “evolutionary approach”
to the quantification of operational risk capital. In essence, it specifies
three approaches, based on the supposition that the appropriate capital
charge for a typical bank will diminish as the bank takes progressive steps
to address operational risk. This essentially allows banks to make increasingly large discounts to their regulatory capital as they make demonstra-
Operational Risk
ble progress toward a well-managed and properly controlled operating
environment. Given that banks today vary widely in their preparedness,
different banks will start at different points on the scale.
Work on operational risk is in a developmental stage, but three different approaches have been identified (in order of increasing sophistication:
basic indicator, standardized, and internal measurement; see Figure 4-11).
1. The basic indicator approach utilizes one indicator of operational risk for a bank’s total activity.
2. The standardized approach specifies different indicators for different business lines.
3. The internal measurement approach requires banks to utilize
their internal loss data when estimating required capital.
Based on work to date, the committee expects operational risk to
constitute on average approximately 20 percent of the overall capital requirements under the new framework. It will be important to collect sufficient loss data in the coming months to establish the accurate calibration
of the operational risk charge as a basis for allowing the more advanced
F I G U R E 4-11
Capital requirement
Operational Risk Approaches and Industry Trend.
Risk sensitivity
332 Basic Indicator Approach
The basic indicator approach (BIA),18 also known as the single indicator
approach, is designed for less sophisticated (and usually smaller) banks.
This method allocates risk capital based on a single indicator of operational risk, the default being gross revenue. It is unclear whether gross
revenue is a relevant indicator for operational risk. The single indicator
approach is considered the easiest to implement, because it specifies a single number across the organization based on a well-known quantity. In
order to satisfy this approach, banks will not have to do anything! However, all other things being equal, the BIA will likely result in higher capital charges than the other two approaches, and the hope is that banks will
try to reduce these by moving up the evolutionary ladder—that is, by
demonstrably improving their management of operational risk.
Within each business line/risk type combination, a supervisor
provides the exposure indicator (EI), which is the proxy for the
size (or amount of risk) of each business line’s operational risk
exposure to each risk type.
A single risk indicator (e.g., gross income) is used as a proxy for
the institution’s overall operational risk exposure.
C = α ⋅ gross income
where α is fixed at 30 percent of gross income. Standardized Approach
The standardized approach19 is the one the Basel Committee recommends
that larger and more global banks use for the time being. It is also the approach that middle-tier banks should target in order to reduce their capital
charges. While the single indicator approach is a crude, across-the-board
measure, the standardized approach is based on information gathered
from individual business units. It is suggested in the consultative paper
that this approach best reflects the actual level of risk within a complicated
organization with a variety of business activities, but does not require invoking complex and still controversial mathematical models.
The standardized approach is inevitably more complicated than the
single indicator approach. The basic principle is that banks will have to
map their own business units into a standard set of business units defined
by the regulator. Each of these standard units is associated with a particular financial indicator—for example, the amount of assets under management for an asset management business—and the associated capital
charge is defined by the level of these indicators:
Bank activities are divided into standardized business units and
business lines.
Operational Risk
A supervisor specifies an exposure indicator (EI) for each
respective business line/risk type combination.
Banks provide indicator data (e.g., gross revenue).
There is an opportunity to migrate (on a business line basis)
toward increasingly more sophisticated approaches.
C = 冱 βi ⋅ EIi
[20% current total MRC, $] ⋅ [business line weighting, %]
βi = ᎏᎏᎏᎏᎏᎏᎏ (4.7)
冱 financial indicator for the business line from bank sample, $
i = business line
β = capital factor (see Table 4-3)
EI = exposure indicator
MRC = minimum regulatory capital
This approach makes progress toward reflecting the makeup of an
individual institution’s business, making it a better measure than the onesize-fits-all approach based on gross revenue. Banks considering this approach will have good reason to start thinking about their business lines’
T A B L E 4-3
Capital Factors for Individual Business Lines
Business Unit
Investment banking
Business Line(s)
Corporate finance
Gross income
Trading and sales
Gross income (or VaR)
Retail banking
Annual average assets
Commercial banking
Annual average assets
Payment and settlement
Annual settlement
Retail brokerage
Gross income
Asset management
Total funds under
Bank for International Settlement (BIS), Basel Committee on Banking Supervision, The New Basel Capital
Accord, Consultative Document, Issued for Comment by 31 May 2001, Basel, Switzerland: Bank for International
Settlement, January 2001, para. 26.
operational risks and how they might be best managed, but will not have
to go through the laborious and complicated exercise of collecting and
evaluating internal loss data required under the third and most sophisticated approach.
The problem with the first and second methods is that they assume
operational risk is linear and directly related to the size of the institution
or business line. The concern about the third method is that it posits a
fixed relationship between expected and unexpected losses that most experts in the field simply do not believe exists.
For the purposes of consistent and structured measurement of loss
events, Basel breaks down operational risk loss experiences into the following loss types:20
Write-downs. Direct reduction in value of assets due to theft,
fraud, unauthorized activity, or market and credit losses resulting
from operational events
Loss of recourse. Payments or disbursements made to incorrect
parties and not recovered
Restitution. Restitution paid to clients in the form of principal
and/or interest, or the cost of any other form of compensation
paid to clients
Legal liability. Judgments, settlements, and other legal costs
Regulatory and compliance. Fines, or the direct cost of any other
penalties, such as license revocations
Loss of or damage to assets. Direct reduction in the value of
physical assets, including certificates, due to some kind of
accident (e.g., neglect, fire, earthquake)
The standard approach has not yet demonstrated how existing business fields (e.g., private banking) can be mapped into the preexisting business unit schema from the BIS. Business fields such as agency business,
custody, etc. do not fit into the existing schema. The BIS wants to create
additional business units. Internal Measurement Approach
The internal measurement approach (IMA)21 is reserved for banks with
the most sophisticated risk management controls and programs in place.
This approach breaks down the idea of indicators still further by introducing the concept of risk types. A bank needs to provide an exposure indicator for each risk type (tied to individual business units) based on
internal loss data and the probability of a loss event occurring. This allows
banks to align the capital charge for operational risk more closely with the
actual economic risks of their business, in a way that reflects both their
track record and their current operating environment.
Operational Risk
No more than a handful of banks would qualify for this approach
today, largely because of the lack of appropriate data. The Basel Committee recognizes that banks will move toward this approach as they start collecting internal loss data, and that this will be a step-by-step process.
Among the tasks that need to be undertaken are the establishment of industry standards for loss data and the collection of a critical mass of loss
data by pooling internal loss information from a number of institutions:
The same business lines as in the standardized approach
Based on internal data, banks’ measurements of parameters and
calculation of expected capital requirement:
[γi,j ⋅ EIi,j ⋅ PEi,j ⋅ LGEi,j]
where γ = conversion (translation) factor for the calculation of the capital
requirements based on the expected loss
EI = exposure indicator (risk indicator), which is an estimate for the risk
exposure per business line
PE = probability of loss event, an estimate for the frequency of a loss
LGE = loss given event, an estimate for the effective loss impact
i = index for the corresponding business line
j = index for the corresponding risk factor
4.11.3 Operational Risk Standards
The accord is quite demanding in regard to the operational risk standards
that have to be applied. These qualifying criteria cover such areas as effective risk measurement and control, measurement, and validation.22
Regarding operational risk standards, the standardized approach requires:23
Independent risk control and audit functions
Effective use of risk reporting systems
Appropriate documentation of risk management systems
Independent operational risk management and control processes
covering design, implementation, and review of operational risk
measurement methodology
Periodic reviews by internal auditors
Development of specific, documented criteria for mapping current
business lines and activities into the standardized framework
The internal measurement approach (IMA) requires regarding operational risk standards,24 accuracy of loss data, and confidence in the re-
sults of calculations using that data (including PE and LGE), which must
be established through “user tests”:
Banks not fully integrating IMA methodology into their day-today activities and major business decisions will not qualify for
this approach.
Appropriate historical loss experiences must be identified that are
representative of current and future business activities.
Periodic verification processes for estimating parameter inputs to
regulatory capital charge must be performed and validated.
Supervisory review and validation must be performed.
It can be assumed that the vast majority of regulated financial organizations will be most interested in the standardized approach—either
aspiring to it, in the case of smaller organizations, or ensuring compliance
with it, in the case of medium-sized and larger institutions. The standardized approach is in any case a natural precursor to the internal measurement approach, so even banks with more aggressive goals will find it
useful to initially work through the requirements of the standardized approach.
Assuming that an acceptable form of the standardized approach is
eventually implemented, where does that leave the banks? It is likely
that many will fall into the first tier in the beginning and will be hit with
the highest capital charges. It is also possible that many moderately sophisticated banks will be able to move quite quickly into the second tier
once they have demonstrated they have the proper controls in place. In
order to qualify for this stage, the banks will have to demonstrate the establishment of an operational risk management and control process, and
a strategy for mapping an individual bank’s business lines into the standardized formula. The BIS suggests the adoption of numerous qualitative items in a bank’s quest to manage its operational risks. These items
The establishment of a risk reporting system
The establishment of an independent operational risk
management and control process (which usually involves
either a risk management, internal audit, or financial
operations function)
The identification of those historical loss events that
are appropriate for an individual institution and its
business units (which involves the use of an external loss
The business line controversy is not covered in this book. For details,
refer to the committee’s publications covering this issue.
Operational Risk
4.11.4 Possible Role of Bank Supervisors
The discussion about the possible role of bank supervisors reflects the relatively early stage of the development of operational risk measurement and
monitoring. Most banks agree that the process is not sufficiently developed
to enable bank supervisors to mandate guidelines specifying particular
measurement methodologies or quantitative limits on risk. Preference was
expressed at this stage for supervisors to focus on qualitative improvement
in operational risk management. At this stage, bank supervisors should become increasingly aware of the existence and importance of operational
risk. As standards do not yet exist, financial institutions are skeptical about
best-practices standards, given the perceived institution-specific nature of
operational risk.
While the debate over operational risk has only just begun, the prospect of
specific capital charges for operational risk looks inevitable. The scale and
complexity of the underlying industry risks, and the systemic effect of
losses incurred to date, are too large for regulators to ignore. Moreover,
market and credit risk capital guidelines would be incomplete in the absence of an operational risk element.
However, no single approach to operational risk capital allocation
has yet been adopted and implemented by a critical mass of institutions.
This makes the supervisory task of devising such a method challenging, to
say the least. And the challenges (in academia and in practice) are not limited to determining the formulae that underlie capital models; they also
involve the quality and consistency of operational risk data in individual
institutions and across the industry.
A key consideration will be whether the methodologies selected by
regulators encourage operational risk mitigation on both institutional and
industrywide levels. A badly designed set of capital regulations would
spawn operational risk measurement functions within financial institutions, but would not promote effective risk mitigation and management
Managing operational risk is becoming an important feature of
sound risk management practice in modern financial markets. The most
important types of operational risk involve breakdowns in internal controls and corporate governance. As recent cases in the market show, such
breakdowns can lead to financial losses through error, fraud, or failure to
perform in a timely manner or can cause the interests of the bank to be
compromised in some other way (for example, dealers, lending officers, or
other staff exceeding their authority or conducting business in an unethical or risky manner). Other aspects of operational risk include major fail-
ure of information technology systems or inability to report in a timely
manner to investors, regulators, and clients.
The regulatory incentive takes the form of capital allocation for operational risk. In contrast, the management incentive consists of incorporating operational risk measurement into the performance evaluation
process or requiring business line managers to present operational loss
details and resultant corrective action directly to the bank’s highest levels
of management. While most banks have some framework for managing
operational risk, many banks indicate that they are only in the early stages
of developing an operational risk measurement and monitoring framework. Few banks currently measure and report this risk on a regular basis,
although many track operational performance indicators, analyze loss experiences, and monitor audit and supervisory ratings. While the industry
is far from converging on a set of standard models, such as are increasingly available for market and credit risk measurement, many banks have
developed or are developing models relying on a surprisingly similar set
of risk factors. Those factors include internal audit ratings or internal control self-assessments; operational indicators such as volume, turnover, or
rate of errors; loss experience; and income volatility.
This chapter focuses on the origins of operational risk, the potential
development path for operational risk models and approaches, and the
regulatory framework from the Bank for International Settlement, as outlined in the latest version of the New Basel Capital Accord, which will
force banks to measure operational risk with one of three alternative
measurement approaches and to support operational risk with capital.
Core elements discussed in this chapter are the alternative methodologies for measuring operational risk and the framework for measuring
and supporting operational risk from a regulatory standpoint.
4.13 NOTES
1. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Operational Risk Management, Basel, Switzerland: Bank for
International Settlement, September 1998.
2. British Bankers’ Association, “Operational Risk Management Study,”
London: British Bankers’ Association, December 1999.
3. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Operational Risk, Consultative Document: Supporting Document to
the New Basel Capital Accord, Issued for Comment by 31 May 2001, Basel,
Switzerland: Bank for International Settlement, January 2001.
4. See also British Bankers’ Association, Operational Risk: The Next Frontier,
London: British Bankers’ Association, December 1999. This study is based
on a series of interviews with 55 global financial institutions located in
North America, Europe, and Asia, and includes a discussion of operational
risk, management structures, senior management reporting, operational
Operational Risk
risk capital, insurance strategies, and tools. An executive summary and
table of contents are available at the British Bankers’ Association Web site
( The report concludes with an
observation of seven major trends, including an industrywide acceptance of
operational risk management as a core competency.
Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Operational Risk, Consultative Document: Supporting Document to
the New Basel Capital Accord, Issued for Comment by 31 May 2001, Basel,
Switzerland: Bank for International Settlement, January 2001, para. 21ff.
Reto R. Gallati, Methodology for Operational Risk, Zurich: KPMG, July 1998.
Andrew Smith, Operational Risk Management—Further Analytical Tools,
London: KPMG, January 1997.
KPMG Peat Marwick, “Operational Risk, Control Benchmarking
Questionnaire,” KPMG, March 1997.
Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Core Principles for Effective Banking Supervision, Basel,
Switzerland: Bank for International Settlement, September 1997, para. 13.
See the FSA Web site ( for additional information.
See the Bank of Japan Web site (
fwp0003.html), “Challenges and Possible Solutions in Enhancing
Operational Risk Measurement.”
For a statement regarding the future revision of the Capital Adequacy
Directive framework and operational risk, see the Swiss Federal Banking
Commission Web site (
For further details on Banco Ambrosiano and the Vatican Bank, see
For further details, see the BBA Web site (, “BBA
Operational Risk Database Association” and “BBA/ISDA/RMA
Operational Risk Research.”
Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Basel Capital Accord of July 1988, Basel,
Switzerland: Bank for International Settlement, April 1998.
Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Operational Risk, Consultative Document: Supporting Document to
the New Basel Capital Accord, Issued for Comment by 31 May 2001, Basel,
Switzerland: Bank for International Settlement, January 2001, para. 15ff.
Ibid., para. 22f.
Ibid., para. 24ff.
Ibid., annex 4.
Ibid., para. 31ff.
Ibid., para. 51ff.
Ibid., para. 43f.
Ibid., para. 44ff.
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Building Blocks
for Integration of
Risk Categories
he integration of market, credit, and operational risk into a holistic risk
management framework depends on the compatibility of the assumptions, conditions, and parameters of the individual risk categories. As all
individual risk categories have, to a large extent, evolved naturally, the assumptions, conditions, and parameters linked with the risk categories are
different. Any attempt to integrate the individual risk categories must involve verifying the compatibility of the different assumptions, models,
and approaches. Currently, the biggest supporters of an integrated approach are the regulators.
The New Basel Capital Accord1 attempts to unify the three risk categories with the purpose of supporting the risk of a financial organization
with capital, based on models for market, credit, and operational risk. It is
not an attempt to unify the models. Nevertheless, we will use the regulatory framework as a benchmark for comparing the different risks. The development of an integrated approach has not yet emerged, but, as with
any complex development, it is just a question of time until the different
risk dimensions are linked in a more coherent manner.
The discussion in this chapter deals with the basics of risk category
integration; in Chapter 6 we will explore more integrated methodologies.
Figure 5-1 highlights the typical development of a risk management
practice. The future development will definitely depend largely on the
agreed-upon and standardized definition and assumptions underlying
the individual risk models. Today’s “integrated risk management solutions” are really individual risk dimensions (such as market risk) deployed
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F I G U R E 5-1
Development Stages of Risk Management.
Initial stages
Holistic risk
Maturity level
Development stages of risk management practice
across a company rather than a holistic risk framework. To better understand the possibilities of integrated risk management, and the conflicts between different approaches from different risk dimensions, this chapter
presents different assumptions, models, and approaches and examines
how, if, and to what extent the three risk dimensions can be integrated.
The New Basel Capital Accord is used as a benchmarking framework in this chapter, while the individual approaches to calculating and
supporting risk with capital (such as VaR for market risk) are analyzed in
other chapters (e.g., Chapter 2 on market risk).
5.2.1 Background
The New Basel Capital Accord2 contains for the first time an integrated
approach, attempting to bring together market, credit, and operational
risk in order to calculate the overall risk exposure of a bank and to derive
the required (regulatory) capital to support the bank’s specific risk profile.
Therefore, the Accord is explained in some detail in this chapter as well as
in Chapters 2, 3, and 4.
More than a decade has passed since the Basel Committee on Banking Supervision introduced its 1988 capital accord. The New Basel Capital
Accord has emerged over the past years, evolving from the 1988 Capital
Building Blocks for Integration of Risk Categories
July 1988
End of 1992
June 1999
January 2001
Late May 2002
End of 2002
Current accord published
Deadline for implementation
First consultative package on the new accord
Second consultative package
Deadline for comments
Publication of the new accord3
Implementation of the New Basel Capital
The new framework intends to provide approaches that are more
comprehensive and more sensitive to risks than the 1988 accord, while
maintaining the overall level of regulatory capital (see Table 5-1). Capital
requirements reflect the underlying risks banks will allow in order to
manage their businesses more efficiently.
The new framework’s focus is primarily on internationally active
banks. However, its underlying principles are intended to be suitable for application to banks of varying levels of complexity, sophistication, and size.
The new framework is less prescriptive than the original accord. At
its simplest level, the new framework is somewhat more complex than the
old one, but it offers a range of approaches to enable banks to use more
risk-sensitive analytical methodologies (see Table 5-2). These inevitably
require more detail in their application and thus a thicker rule book.
5.2.2 Existing Framework
The 1988 Accord focused on the total amount of bank capital, which is
vital for reducing the risk of bank insolvency and the potential cost to depositors of a bank’s failure. Building on this, the intent of the new framework is to improve the safety and soundness of the financial system by
T A B L E 5-1
Rationale for a New Accord: Need for More Flexibility and Risk Sensitivity
Existing Accord
Proposed New Accord
Focus on a single risk measure
More emphasis on banks’ own internal
methodologies, supervisory review, and
market discipline
One size fits all
Flexibility, menu of approaches, incentives
for better risk management
Broad structure
More risk sensitivity
T A B L E 5-2
Key Issues for Banks and Supervisors
Key Issues and Challenges
for Supervisors
Reliability of banks’ internal ratings
Validation of risk factors through the
business cycle
Historical data and changes in products/
risk exposures
Assessment of business practices and
examiner resources
Treatment of small business loans and
project finance and equity exposures
Calibration capital across the 6
exposure types
Diversification benefits and proposed
granularity adjustment
Rewarding use of internal rating–based
(IRB) approach while leaving capital in
the banking system unchanged
Key Issues and Challenges
for Banks
Data collection and consistency
• Establishing consistent ratings
across business lines
• Linking ratings and default
• Collecting sufficient data over the
business cycle
Risk factor validation and adjustments
for point in business cycle
Disclosure requirements
• Collection for dissemination in a
timely manner
• Comparability across institutions
Requirement for rapid rollout of
advanced IRB once started
90% floor on advanced IRB provides
adequate incentive?
Assessment of economic capital and
capital allocation
placing more emphasis on a bank’s own internal control and management, the supervisory review process, and market discipline.
The 1988 Accord essentially provided only one option for measuring
the appropriate capital. However, the best way to measure, manage, and
mitigate risks differs from bank to bank. An amendment was introduced
in 1996 that focused on trading risks and allowed some banks for the first
time to use their own systems to measure their market risks.4
The new framework provides a spectrum of approaches with different levels of complexity, from simple to advanced methodologies, for the
measurement of both credit risk and operational risk in determining capital levels. It provides a flexible framework in which financial organizations, subject to supervisory review, will adopt approaches that best fit
their business strategies, level of sophistication, and risk profile. The
framework also deliberately provides embedded rewards for stronger and
more sophisticated risk measurement.
The 1988 accord requires internationally active banks in the G-10
countries to hold capital equal to at least 8 percent of a group of assets
Building Blocks for Integration of Risk Categories
measured in different ways according to their level of risk. The definition
of capital is set (broadly) in two tiers. Tier 1 is shareholders’ equity and retained earnings, and Tier 2 is additional internal and external resources
available to the bank. The bank also has to hold at least half of its measured capital in Tier 1 form.
A portfolio approach is applied to the measurement of risk, with assets classified into four categories or “buckets” (0 percent, 20 percent, 50
percent, and 100 percent) according to the debtor category. This means
that some assets (essentially bank holdings of government assets such as
Treasury bills and bonds) have no capital requirement, while claims on
banks have a 20 percent weight, which translates into a capital charge of
1.6 percent of the value of the claim. However, virtually all claims on the
nonbank private sector receive the standard 8 percent capital requirement.
There is also a scale of charges for off-balance-sheet exposures through
guarantees, commitments, forward claims, etc. This is the only complex section of the 1988 accord and requires a two-step approach whereby banks
convert their off-balance-sheet positions into a credit equivalent amount
through a scale of conversion factors, which are then weighted according to
the counterparty’s risk weighting.
The 1988 accord has been supplemented a number of times, with
most changes relating to the treatment of off-balance-sheet activities. A
significant amendment was enacted in 1996, when the Committee introduced a measure whereby trading positions in bonds, equities, foreign exchanges, and commodities were removed from the credit risk framework
and given explicit capital charges related to the bank’s open position in
each instrument.
Impact of the 1988 Accord
The two principal purposes of the accord were to ensure an adequate level
of capital in the international banking system and to create a “more level
playing field” in competitive terms so that banks could no longer build
business volume without adequate capital backing. These two objectives
have been achieved. The merits of the accord were widely recognized, and
during the 1990s the accord became an accepted world standard, with
well over 100 countries applying the Basel framework to their banking
systems. However, there also have been some less positive features. The
regulatory capital requirement has been in conflict with increasingly sophisticated internal measures of economic capital. The simple bucket approach with a flat 8 percent charge for claims on the private sector has
given banks an incentive to move high-quality assets off the balance sheet,
thus reducing the average quality of bank loan portfolios. In addition, the
1988 Accord does not sufficiently recognize credit risk mitigation techniques, such as collateral and guarantees. These are the principal reasons
why the Basel Committee decided to propose a more risk-sensitive framework in June 1999.
The June 1999 Proposal
The initial consultative proposal had a strong conceptual content and was
deliberately rather vague on some details in order to solicit comment at a
relatively early stage of the Basel Committee’s thought process.5 It contained three fundamental innovations, each designed to introduce greater
risk sensitivity into the accord. One was to supplement the current quantitative standard with two additional pillars dealing with supervisory review and market discipline. These were intended to reduce the stress on
the quantitative Pillar I by providing a more balanced approach to the capital assessment process. The second innovation was that banks with advanced risk management capabilities would be permitted to use their own
internal systems for evaluating credit risk, known as internal ratings, instead of standardized risk weights for each class of assets. The third principal innovation was to allow banks to use the gradings provided by
approved external credit assessment institutions (in most cases private
rating agencies) to classify their sovereign claims into five risk buckets
and their claims on corporations and banks into three risk buckets. In addition, there were a number of other proposals to refine the risk weightings and introduce a capital charge for other risks. The basic definition of
capital stayed the same.
The comments on the June 1999 paper were numerous and reflected
the important impact the 1988 accord has had. Nearly all those who commented welcomed the intention to refine the Accord and supported the
three-pillar approach, but there were many comments on the details of the
proposal. In particular, a widely expressed comment from banks was that
the threshold for the use of the IRB approach should not be set so high as
to prevent well-managed banks from using their internal ratings. Intensive work has taken place in the 18 months since June 1999. Much of this
has been leveraged off work undertaken in parallel with industry representatives, whose cooperation has been greatly appreciated by the Basel
Committee and its Secretariat.
As the U.S. energy markets discovered recently, the law of unintended consequences is the only certainty in any big regulatory upheaval.
But some things seem pretty certain (see Table 5-3).
The New Basel Capital Accord tries to achieve the following objectives:
Use three mutually reinforcing pillars to more closely align
regulatory capital with economic capital
Encourage integration of risk assessment into the management
Building Blocks for Integration of Risk Categories
T A B L E 5-3
Meaning of the New Accord
Basel II will mean:
A much greater variance in capital requirements between
banks with different kinds of businesses, from retail to
A more complex regulatory regime, with banks and national
jurisdictions likely to vary much more in the regulatory
capital rules they follow and the quality of their enforcement
A convergence (if incomplete) between economic capital
(true cost of risk) and regulatory capital, and the
introduction into bank regulations of many sophisticated risk
concepts that will be the building blocks of future regulatory
Because Basel II will:
Allow qualifying banks to use internal ratings and economic
capital concepts to measure regulatory capital for credit risk
Set a specific charge for operational risk and allow
qualifying banks to choose between more or less
sophisticated ways of measuring this
Oblige banks to release risk information to analysts that
might affect bank share prices and credit ratings
Basel II will not:
Alter the way banks set aside capital for market risk, or
change the kinds of capital that count as regulatory capital
Allow banks to use internal portfolio models for either credit
or operational risk—yet
Alter the total amount of capital that the banking industry
sets aside, providing the regulators get their sums right
Achieve greater credit risk sensitivity
Create flexibility in selecting approaches to setting regulatory
Establish dynamic risk measurement methods for setting
regulatory capital
Reward institutions that adopt more sophisticated risk
assessment techniques in order to assess the risks more
Apply an explicit capital charge for operational and all other
risks, and thus reduce the need for a capital “cushion” (reserves)
Maintain competitive equity between banks and nonbanks and
across instrument types and national jurisdictions
The New Basel Capital Accord has still failed to address the following issues:
The great degree to which the final figure for regulatory capital
will diverge from that implied by economic capital calculations
Definition and mechanics of the proposed charge for operational
Treatment of retail portfolios
Treatment of credit derivatives
Proposed maturity factors for loan portfolios
Lack of incentives to progress from basic to sophisticated risk
Basel has indicated that it expects aggregate levels of regulatory capital
to remain broadly steady; however, individual banks may well find themselves holding more or less regulatory capital than under the 1988 accord.
5.2.5 Potential Modifications
to the Committee’s Proposals
The Basel Committee has set as a standard that its next consultative paper
must reflect the best possible effort to construct a revised accord that
meets its objectives. Accordingly, the committee now plans to undertake
an additional review aimed at assessing the overall impact of a new accord on banks and the banking system before releasing the next consultative paper. The committee’s work during this quality assurance phase will
focus on three issues:6
1. Balancing the need for a risk-sensitive accord with the need to
make it sufficiently clear and flexible so that banks can apply it
2. Ensuring that the accord leads to appropriate treatment of credit
to small- and medium-sized enterprises, which are important
for economic growth and job creation
3. Finalizing calibration of the minimum capital requirements to
bring about a level of capital that, on average, is approximately
equal to the requirements of the present Basel Accord, while
providing some incentive to those banks using the more risksensitive internal ratings–based system
The Committee is undertaking a comprehensive quantitative impact
study simultaneously during the next consultation period and believes
that performing the impact assessment will help make the consultation
period more constructive. On October 1, 2002, the Basel Committee on
Banking Supervision launched a comprehensive field test for banks of its
proposals for revising the 1988 capital accord. The field test, referred to as
the third Quantitative Impact Survey or QIS3, is focused on the proposed
minimum capital requirements under Pillar I of the New Basel Capital Ac-
Building Blocks for Integration of Risk Categories
cord. Banking organizations participating in the QIS3 were to submit completed questionnaires to their national supervisors by December 20, 2002.7
Undertaking this additional review means that the committee’s next consultative paper will not be issued in early 2002, as previously indicated.
Instead, the committee will first seek to specify a complete version of its
proposals in draft form, including those areas subject to modifications,
such as asset securitization and specialized lending. Once a draft version
of a fully specified proposal has been completed, the committee will undertake a comprehensive impact assessment of the draft proposal.
After incorporating the results of its comprehensive impact assessment, the committee will release these proposals to be reviewed during a
formal consultation period. All interested parties will be invited to provide
comment on this consultative paper. The committee intends to finalize the
New accord following the completion of the formal consultation period.
The Basel Committee has previously announced its intention to finalize the
New accord in 2002 and for member countries to implement the New accord in 2005. The committee does not believe that its additional review
process will be a lengthy one, and therefore is not at this time announcing
a revised schedule for completion or implementation of the New accord.
In terms of potential modifications to the committee’s proposals, it is
important to note several of the potential changes that have already been described in working papers, press releases, and the results of the quantitative
impact studies issued over the last few months.8 These include the following:
Modifications related to the coverage of expected losses,
including the use of excess general provisions, specific
provisions, and margin income (under certain circumstances)
to offset IRB capital requirements
Modifications to the proposed treatment of operational risk,
including the introduction of the advanced measurement
approach (AMA) and the reduction in the proposed target of
operational risk capital as a percentage of current minimum
capital requirements from 20 percent to 12 percent (with a further
reduction potentially available under the AMA approach)
Modifications to the credit risk mitigation framework such that
residual risks will be assessed through Pillar II and the w factor
will be eliminated from Pillar I of the framework
Further specification of proposals relating to equity positions
held outside the trading book, specialized lending exposures, and
In addition to these developments, the quantitative impact exercise
seeks to assess the impact of other possible modifications to the committee’s proposals, including:
A modified risk weight curve for all corporate, sovereign, and
interbank portfolios. The effects of this modified risk weight
curve would also flow through to other portfolio treatments that
are defined relative to the corporate IRB risk weights, including
aspects of the securitization, equity, and specialized lending
Greater recognition of physical collateral and receivables.
Modified risk weight curves for both residential mortgage
exposures and other retail exposures.
In April 2001, the Basel Committee on Banking Supervision initiated
a Quantitative Impact Study (QIS2) involving a range of banks across the
G-10 and beyond.9 The objective of the study was to gather the data necessary to allow the committee to gauge the impact of the proposals for
capital requirements set out in the January 2001 second consultative paper
(CP2). An earlier, more limited study (QIS1) had been carried out in 2000
to inform the CP2 calibration.10
On average, the QIS2 results indicate that the CP2 proposals for
credit risk would create an increase in capital requirements for all groups
under both the standardized and IRB foundation approaches. Indeed, the
foundation approach would generate higher capital requirements than the
standardized approach, counter to the committee’s desired incentives.
Across the G-10, Group 1 banks’ minimum capital requirements under the
standardized approach would be 6 percent higher on average. Under the
IRB foundation approach, minimum requirements would be 14 percent
higher. Requirements seem likely to be lower under the IRB advanced approach, with an average change of −5 percent. For G-10 Group 2 banks,
which would be more likely to use the standardized approach, the average
increase in capital would be 1 percent. Results for Group 1 EU banks are
similar, with increases of 6 percent and 10 percent under the standardized
and IRB foundation approaches, respectively, but with a smaller change of
−1 percent under the IRB advanced approach. For banks outside the G-10
and EU, the increase under the standardized approach was 5 percent on
These results do not include any charge for operational risk. As reported in a June 25, 2001 press release (available at
p010625.htm), the committee has concluded that its original target proportion of regulatory capital related to operational risk (i.e., 20 percent)
will be reduced because this reflects too large an allocation of regulatory
capital to this risk. For purposes of this exercise, and to illustrate the potential impact of the operational risk capital charge, Table 5-4 reflects an
operational risk charge of 12 percent of current minimum regulatory capital for the standardized approach and 10 percent for the IRB approaches.
Building Blocks for Integration of Risk Categories
T A B L E 5-4
Percentage Change in Capital Requirements Under the Second
Consultative Proposal
IRB Foundation
IRB Advanced
G-10 Group 1
G-10 Group 2
EU Group 1
EU Group 2
Other (non-G-10,
The committee has assumed that for the standardized approach on credit
risk the standardized charge for operational risk will apply (i.e., 12 percent). For the IRB approaches, the figure of 10 percent has been used only
as a working assumption for the purpose of this exercise. For further information, see also the Basel Committee’s working paper on the regulatory treatment of operational risk at
The quantitative impact study for operational risk has delivered no
clear direction regarding capital support for operational risk.11 The study
demonstrates the effort needed regarding data quality, standardization of
units, formats (currencies, units, etc.), consistency checks, and so on.
Based on the results of the QIS2 exercise for operational risk, a new
impact study regarding operational risks is required. The focus of the
committee is on how any future QIS exercises might be improved to make
them less burdensome both for the participating banks and in working
with the submitted data and to enhance the value of the information received through the exercise. In this regard, the Committee is still open for
feedback from the banking industry and other interested parties on the
process of collecting this data and on the actual data collected, with the
hope of identifying improvements that could be made in structuring any
future rounds of QIS data requests on operational risk.
In considering the issues raised dealing with data and process problems regarding operational risk, it is important to note that the focus of
any future QIS exercises for operational risk has not yet been determined.
Nor has the scope of data to be requested—which might, for instance, include internal capital allocation information, exposure indicators, and/or
loss event information—been decided on.
The three pillars of the new accord are:
Pillar I. Minimum capital requirement (capital adequacy for
market, credit, operational risk) due to increasing risk sensitivity
and flexibility through updated standardized and new IRB
Pillar II. Supervisory review process consisting of encouraging
banks to develop and use better risk management techniques to
monitor and manage risks; to review risk assessment and the
level of integration into management reporting, decision making
and processes; and to create a mechanism for regulators to
require greater capital.
Pillar III. Market discipline created by reinforcing capital
regulation and other supervisory efforts to ensure safety and
These three mutually reinforcing pillars together should contribute
to the safety and soundness of the financial system. The Committee
stresses the need for rigorous application of all three pillars.
Pillar I: Minimum Capital Requirement
The Pillar I establishes minimum capital requirements. The new framework maintains both the current definition of capital and the minimum requirement of 8 percent of capital to risk-weighted assets. To ensure that
risks within the entire banking group are considered, the revised accord
will be extended on a consolidated basis to holding companies of banking
groups. (The Accord contains a discussion of the treatment of holdings
and related issues.)
The committee’s goal remains the same as detailed in the June 1999
paper: namely, to neither raise nor lower the aggregate regulatory capital,
inclusive of operational risk, for internationally active banks using the
standardized approach. With regard to the IRB approach, the committee’s
ultimate goal is to ensure that the regulatory capital requirement is sufficient to address underlying risks and contains incentives for banks to migrate from the standardized approach to the IRB approach. The committee
invites the industry’s cooperation in conducting the extensive testing and
dialogue needed to attain these goals.
The capital adequacy is measured as follows:
Total capital (unchanged)
ᎏᎏᎏᎏ = capital ratio (minimum 8%)
Market + credit + operational risk
Building Blocks for Integration of Risk Categories
T A B L E 5-5
Menu of Alternative Approaches for the Different Risk Categories
Market Risk
Choice of approaches to
measure market risk
Internal models
Credit Risk
Choice of approaches to
measure credit risk:
approach (a modified
version of the existing
Foundation IRB
Advanced IRB
Operational Risk
Choice of approaches to
measure operational risk:
Basic indicator
Internal measurement
Table 5-5 shows the menu to chose from regarding the different approaches within the different risk categories.
The enhancement within the new accord focuses on improvements
in the measurement of risks, i.e., the calculation of the denominator of the
capital ratio. The credit risk measurement methods are more elaborate
than those in the current accord. The new framework proposes for the first
time a measure for operational risk, while the market risk measure remains unchanged.
5.3.2 Pillar II: Supervisory Review Process
Pillar II13 focuses on the supervisory process to be implemented on a national level. The supervisory review process requires supervisors to ensure that each bank has sound internal processes in place to assess the
adequacy of its capital based on a thorough evaluation of its risks. Banks
must have a process for assessing overall capital adequacy based on:
Board and senior management oversight
Sound capital assessment
Comprehensive assessment of risks
Monitoring and reporting
Internal control review
The New Accord demands that local regulators (supervisors) review
and evaluate a bank’s assessments and strategies, that the bank operate
above minimum regulatory capital ratios, and that supervisors intervene
at an early stage.
The new framework stresses the importance of bank management
developing an internal capital assessment process and setting targets for
capital that are commensurate with the bank’s particular risk profile and
control environment. Supervisors would be responsible for evaluating
how well banks are assessing their capital adequacy needs relative to their
risks. This internal process would then be subject to supervisory review
and intervention where appropriate. The implementation of these proposals will in many cases require a much more detailed dialogue between supervisors and banks. This in turn has implications for the training and
expertise of bank supervisors, an area in which the committee and the
BIS’s Financial Stability Institute will be providing assistance.
This pillar is not a focus area of this book. For further information on
Pillar II, refer to the BIS literature and literature from the industry.
5.3.3 Pillar III: Market Discipline and General
Disclosure Requirements
Pillar III of the new framework14 aims to bolster market discipline through
enhanced disclosure by banks. Effective disclosure is essential to ensure
that market participants can better understand banks’ risk profiles and the
adequacy of their capital positions. The new framework sets out disclosure requirements and recommendations in several areas, including the
ways a bank calculates its capital adequacy and assesses its risks. The core
set of disclosure recommendations applies to all banks, with more detailed requirements for supervisory recognition of internal methodologies
for credit risk, credit risk mitigation techniques, and asset securitization:
Banks should have a formal disclosure policy, approved by the
board of directors, that describes the bank’s objective and
strategy for disclosure of public information about its financial
condition and performance.
Increasingly detailed disclosure requirements will apply for
supervisory recognition of internal methodologies for credit risk,
credit risk mitigation techniques, and asset securitization.
Disclosures will include both core (qualitative and quantitative)
and supplemental components. Additionally, banks will be
required to implement a process for assessing the
appropriateness of disclosure, including frequency. The
verification process has to be performed at least annually.
Disclosure should take place on a semiannual basis at a minimum.
Quarterly disclosure will be expected for internationally active
banks with certain exposures subject to rapid time decay.
The acceptance of IRB approaches is dependent on minimum disclosure requirements (see Table 5-6).
Building Blocks for Integration of Risk Categories
T A B L E 5-6
Core Quantitative and Qualitative Disclosures for IRB Approaches
Core Quantitative Disclosures
Overall risk breakdown of portfolio
Geographic breakdown/concentration of
credit exposures
Broad on/off-balance sheet breakdown
Sector breakdown of credit exposures
(e.g., by industry)
Maturity profile of book
Core Qualitative Disclosures
Structure, management, and
organizational credit risk management
Strategies, objectives, and practices in
managing/controlling credit risk
Information on techniques and methods
for managing past due and impaired
Information on problem loans and
Recommended supplementary disclosures include further detail
regarding the form of credit risk exposures (e.g., loans, commitments,
guarantees, tradable securities, counterparty risk in derivatives) and information about the mitigation of credit risk (securitization, credit derivatives, etc.) (see Table 5-7).
Market discipline is one of the focus areas at the heart of Basel II.
It’s new, it’s trendy, and it should even be cheap. Banks accept that they
will be expected to disclose more about their credit and operational risks
and how they manage them, but they are not satisfied with the level of
detail and the disclosure templates put forward in the regulators’ proposals. The rationale behind the disclosure proposals is that, since banks
are almost invariably ahead of the regulators when it comes to innovation, the best way to regulate a bank’s capital adequacy is to leave it to
the market itself. This does not mean taking an entirely laissez-faire approach to regulation, but allowing competitors, customers, and counterparties to make informed decisions about whether or not to trade with a
particular bank based on its known exposures and the level of capital it
holds to cover them. The regulator’s function becomes one of making
sure that the information is relevant, sufficient, and comparable. The
actual content and extent of the information to be disclosed is hotly debated between players in the industry, regulators, credit agencies, accounting policy-setting bodies, etc. Disclosing information according to
the New Accord guidelines is viewed as disclosing proprietary and confidential information to the public, overloading the shareholders with
information, etc. The industry expects that the regulators will modify
the concept substantially without removing the innovative third pillar of
the proposal.
T A B L E 5-7
Supplementary Disclosures in the New Accord
Scope of application
Strong recommendations
Location in
Supporting Document
Pillar III
Strong recommendations
Pillar III
Credit risk (general)
Strong recommendations
Pillar III
Credit risk (standardized
Requirements and strong
Pillar III
Credit risk mitigation
Requirements and strong
Pillar III
Credit risk (IRB approaches)
Pillar III
Market risk
Strong recommendations
Pillar III
Operational risk
Strong recommendations
and (in future)
Pillar III
Interest rate risk in the
banking book
Strong recommendations
Pillar III
Capital adequacy
Strong recommendations
Pillar III
Asset securitization
Asset securitization
ECAI recognition
Standardized approach
Supervisory transparency
Strong recommendations
Standardized approach
and Pillar II
Bank for International Settlement (BIS), Basel Committee on Banking Supervision, The New Basel Capital Accord,
Consultative Document, Issued for Comment by 31 May 2001, Basel, Switzerland: Bank for International Settlement, January 2001,
para. 633 ff.
This pillar is not a focus area of this book. For further information,
refer to the BIS literature and literature from the industry.
5.4.1 Background
The following discussion of VaR will help readers understand the benefits
and pitfalls of VaR, which is used as a universal measurement in an integrated framework. Identifying and measuring the risks associated with
instruments and participants in the financial markets has become the primary focus of intense study by academics, regulators, and financial insti-
Building Blocks for Integration of Risk Categories
tutions. Certain risks (such as default or counterparty risks) have figured
at the top of most banks’ concerns for a long time, and associated
processes and infrastructures have been reviewed by auditors for a long
time as well. Other risks, such as market risk, have been brought into the
foreground by academic studies on portfolio optimization, derivatives
pricing, and financial scandals, as well as by recent regulatory requirements to support market risks with capital. The reason for the shift in attention lies in the significant changes that the financial markets have
undergone over the last two decades. Historically, risk was viewed from a
nominal perspective, excluding the nature of risk and reduced risk information on pure financial numbers based on net present valuation.
Historical Development of VaR
Financial institutions developed VaR as a general measure of economic loss
that could equate risk across product positions and aggregate risk on a portfolio basis. An important stimulus and condition for the development of VaR
was the move toward marking to market, both for underlying instruments
and derivatives. Prior to that, the focus was on net interest income including
net present values, where the common risk measure was the repricing gap.
Along with technological breakthroughs in data processing, the developments in risk management have gone hand in hand with changes in management practices, including a movement away from risk management
based on accrual accounting and toward risk management based on the
marking to market of positions. Increased liquidity and pricing availability,
along with a new focus on trading, required and led to the frequent revaluation of positions and the concept of marking to market. As investments became more liquid, the need of management to frequently and accurately
report investment gains and losses has led more and more firms to manage
daily earnings from a mark-to-market perspective. The switch from accrual
accounting to marking to market often results in higher swings in reported
gains and losses, thereby increasing the need for managers to emphasize the
volatility of the underlying markets. The markets have not become more
volatile, but the focus on risks through marking to market has highlighted
the volatility of earnings. Given the move to frequently revalue positions,
managers and clients have become more concerned with estimating the potential impact of changes in market conditions on the value of their positions.
Instrument complexity. As trading has increased and structured
fixed-income products have evolved from pure coupon-carrying
instrument, duration analysis has taken over. But duration’s
inadequacies led to the adoption of VaR.
Securitization and securities lending and borrowing. Across
markets, traded securities have replaced many illiquid
instruments. Foreign stocks (using American Depository
Receipts, or ADRs) and loans and mortgages (using CMOs) have
been securitized to permit disintermediation and trading. Global
securities markets have expanded, and both exchange-traded and
over-the-counter (OTC) derivatives have become major
components of the markets, including securities lending and
Performance. Significant efforts have been made to develop
methods and systems to measure financial performance. Indices
for equities, fixed-income securities, commodities, and foreign
exchanges have become commonplace and are used extensively
to monitor returns within and/or across asset classes as well as
to allocate funds. The somewhat one-sided focus on returns,
however, has led to incomplete performance analysis. Return
measurement gives no indication of the cost in terms of risk
(volatility of returns). Studies by Markowitz and others on the
efficient frontier clarify the relation of risk and return, and
demonstrate that higher returns can only be obtained at the
expense of higher risks. While this trade-off is well known, the
risk component of the performance analysis has not yet received
broad attention. Investors and trading managers are searching
for common standards to measure market risks and to better
estimate the risk–return profiles of individual assets or asset
classes. Notwithstanding external constraints from regulatory
agencies, the managers of financial firms have also been
searching for ways to measure market risks, given the
potentially damaging effect of miscalculated risks on company
earnings. The Association for Investment Management and
Research (AIMR) and Global Investment Performance Standard
(GIPS) have established standard criteria for how to measure
performance, including the risk component as input factor for
risk-adjusted performance presentation.15 As a result, banks,
investment firms, and corporations are now in the process of
incorporating measures of market risk into their management
Over the last few years, there have been significant developments in
conceptualizing a common framework for measuring market risk. A wide
variety of approaches to measure return have been developed, but little
has been done to standardize the measurement of risk. Over the last two
decades, many market participants, academics, and regulatory bodies
have developed concepts for measuring risks, mainly market risks, using
a nominal view of risk. Over the last years, two approaches have evolved
as a means to measure market risk: VaR and scenario analysis.
Building Blocks for Integration of Risk Categories
VaR and Modern Financial Management
There are two steps to VaR measurement. First, all positions must be
marked to market (valuation). Second, the future variability of the market
value (volatility) must be estimated. Figure 5-2 illustrates this point. Valuation
Frequently traded positions are valued at their current prices or rates as
quoted in liquid secondary markets. To value transactions for which, in
the absence of a liquid secondary market, no market value exists, the position is mapped into equivalent positions or decomposed into parts for
which secondary market prices exist. The most basic such component is a
F I G U R E 5-2
Steps for VaR Measurement, from Account (Records of Positions) Overvaluation to Risk
Market data feed
correlations, and
Risk measurement for
position / portfolio:
Traded securities
(market price)
Traded securities
Decomposition /
Risk forecast
Balance sheet / NAV
Balance sheet / NAV
1st derivative of assets
• VaR
• Specific risk
• Tracking error
Market risk
2nd derivative of assets
single cash flow with a given maturity and currency of the payor. Most
transactions can be described as a combination of such cash flows and
thus can be valued approximately as the sum of the market values of their
component cash flows. Nonmarketable items, however, have embedded
options that cannot be valued in this simple manner. To value them, expected volatilities and correlations of the prices and rates that affect their
value are required, and an appropriate options pricing model is also required. For some valuations, volatilities and correlations are required. Risk Estimation
Risk estimation is based on the change in values as a consequence of expected changes in prices and rates. The potential changes in prices are defined by either specific scenarios or a set of volatility and correlation
estimates. If the value of a position depends on a single rate factor, then
the potential change in value is a function of the factors in the scenarios or
volatility of that rate. If the value of a position depends on multiple factors, then the potential change in its value is a function of the combination
of factors in each scenario, or of each volatility, and of each correlation between all pairs of factors. Generating equivalent positions on an aggregate
basis facilitates the simulation. As will be shown later, the simulation can
be done algebraically using statistics and matrix algebra or exhaustively
by computing estimated value changes for many combinations of factor
changes. Forecasts of volatilities and correlations play a central role in the
VaR approach. Additional Approaches to Risk Estimation
Different approaches to the VaR calculation are currently being used, and
most practitioners have selected an approach based on their specific
needs, the types of positions they hold, their willingness to trade accuracy
for speed (or vice versa), and other considerations. The models used today
differ on two fronts:
1. How changes in the values of financial instruments are estimated as a result of market movements
2. How potential market movements are estimated
What creates the variety of models currently employed is the fact
that the choices made on the basis of these two parameters can be mixed
and matched in different ways. Estimating Changes in Value
There are basically two approaches to estimating how the value of a portfolio changes as a result of market movements: analytical methods and
simulation methods.
Building Blocks for Integration of Risk Categories
Analytical Methods
The analytical sensitivity approach is based on the following equation:
Estimated value change = f (position sensitivity,
estimated rate/price change)
where the position sensitivity factor determines the relationship between
the value of the instrument and the underlying rate or price (factor), and
the accuracy of the risk approximation with the parameter of the estimation, such as probability. In its simplest form, the analytical sensitivity approach looks like this:
Estimated value change = position sensitivity
⋅ estimated rate change
The value change of a fixed-income instrument can be estimated by
using the instrument’s duration. This linear approximation simplifies the
convex price-yield relationship of a bond, and it is extensively used because the duration often accounts for the most significant part of the risk
profile of a fixed-income instrument. Similar simplifications can be made
for options using the option’s delta for the estimated change in value. The
analytical approach to account for nonlinear relationships between market
value and rate changes (e.g., options) can be extended with the deltagamma approach. The more refined version of the analytical approach
looks like this:
Estimated value change = (position sensitivity1 ⋅ estimated rate change)
+ 1⁄2 (position sensitivity2) ⋅ (estimated rate change)2
In the case of an option, the first-order position sensitivity is the
delta, while the second-order term is the gamma. The analytical approach
requires that positions be summarized in some fashion so that the estimated rate changes can be applied. This process of aggregating positions
is called mapping.
The advantages of analytical models are that they are computationally efficient and they enable users to estimate risk in a timely fashion.
Simulation Methods
The second type of approaches, typically referred to as full valuation models, rely on revaluing a position or a portfolio of instruments under different scenarios. How these scenarios are generated depends on the
application of the models, from basic historical simulation to distributions
of returns generated from a set of volatility and correlation estimates.
Some models include user-defined scenarios that are based on major market events and aimed at estimating risk in crisis conditions. This process is
often referred to as stress testing. Full valuation models enable the user to
focus on the entire distribution of returns instead of a single VaR because
they typically provide a richer set of risk measures. Their main drawback
is the fact that the full valuation of large portfolios under a significant
number of scenarios is computationally intensive and time consuming. Estimating Market Movements
The second discriminant between VaR approaches is how market movements are estimated. There is much more variety here, and the following
is not an exhaustive discussion of current practice.
Parametric Method
The parametric method uses historical time series analysis to derive estimates of volatilities and correlations on a large set of financial instruments.
The parametric method, also called the variance-covariance method, assumes
that the probability distribution of past returns can be modeled to provide
reasonable forecasts of future returns over different time horizons. While
the parametric approach assumes conditional normality of returns, the estimation process for the “normal” variance-covariance approach has to be
refined to incorporate the empirically proven fact that most return distributions show kurtosis and leptokurtosis. These volatility and correlation
estimates can be used as inputs in analytical VaR models and full valuation
Historical Simulation
The historical simulation approach, which is generally used for the full
valuation model, makes no explicit assumptions about the probability distribution of asset returns. In historical simulation, portfolios are valued
under a number of different historical time windows that are user defined.
These lookback periods typically range from six months to two years.
Monte Carlo Simulation
While historical simulation approaches quantify risk by replicating one
specific historical path of market evolution, stochastic simulation approaches attempt to generate many more paths of market returns. These
stochastic returns are generated using a defined stochastic process (for example, they assume that the equity markets follow a random walk) and
statistical parameters that drive the process (for example, the mean µ and
standard deviation σ of the random variable).
The following parameters and assumptions add refinements to the
VaR results generated by the approaches just listed:
Building Blocks for Integration of Risk Categories
Implied volatilities. Looking forward, market returns are
examined to give an indication of future potential return
distributions. Implied volatility is extracted from a specific option
pricing model to generate the market’s forecast of future
volatility. Implied volatilities are often used for the review and
examination of historical volatility to refine the risk analysis.
Implied volatilities are not only used to drive global VaR models
as if all observable options prices on all instruments that compose
a portfolio are analytically available. Unfortunately, the universe
of consistently priced and available options prices is not large
enough. Generally, only exchange-traded options are reliable
sources of prices.
User-defined scenarios. Most risk management models add userdefined rate and price movements to the standard VaR
calculation. Some scenarios are subjectively chosen, while others
are based on parameters derived from past crisis events. The
latter is referred to as stress testing and is an integral part of a
well-designed risk management process and required by
regulation. Selecting the appropriate VaR methodology is not
straightforward. Weighing the advantages and disadvantages of
various methodologies will always be important. Cost-benefit
trade-offs are different for each user, depending on his or her
strategy and position in the markets, the number and types of
instruments traded, and the technology available. Different
choices can be made even at different levels of an organization,
depending on the objectives. While trading desks of an institution
may require precise risk estimation involving simulation on
specific trading positions or portfolios, senior management may
opt for an analytical approach that is cost efficient and timely and
that gives an overview with adequate precision. It is important for
senior management to know whether the risk-adjusted institution
is risking $10 million or $50 million, but it is irrelevant for them to
make the distinction between $10 million and $11 million. This
degree of accuracy at the senior management level is not only
irrelevant, but also may be unachievable operationally or may
require a cost that is not consistent with shareholder value.
Definition of VaR
VaR is defined as the predicted worst-case loss at a specific confidence
level (e.g., 95 percent) over a certain period of time (e.g., 10 days). The elegance of the VaR solution is that it works on multiple levels, from the
position-specific micro level to the portfolio-based macro level using instruments or organizational entities as portfolio positions. VaR has be-
come a common language for communication about aggregate risk taking,
both within and outside of an organization (e.g., with analysts, regulators,
rating agencies, and shareholders).
The application of VaR analysis and reporting has extended from position/portfolio VaR, to nonfinancial organizations, to expanded application of the VaR methodology, such as earnings at risk (EaR), earnings per
share at risk (EPSaR), and cash flow at risk (CFaR). Statistical models of
risk measurement, such as VaR, allow an objective, independent assessment of how much risk is actually being taken in a specific situation. Results are reported in various levels of detail by business unit and in the
aggregate. These measures take into account the corporate environment of
an institution, such as accrual vs. mark-to-market accounting or hedge accounting for qualifying transactions. Furthermore, the focus is now on the
longer-term impact of risk on cash flows and earnings (quarterly or even
annually) in the budgeting and planning process.
There are three major methodologies for calculating VaR, each with
unique characteristics. Parametric VaR is simple and quick to calculate,
but is inaccurate for nonlinear positions. The two simulation methodologies, historical and Monte Carlo, capture nonlinear risks and give a full
distribution of potential outcomes, but require more computational
power. Before calculating VaR, three parameters must be specified: (1)
confidence level, (2) forecast horizon, and (3) base currency. The square
root of time scaling of VaR may be applied to roughly extrapolate VaR to
horizons longer than 1 day, such as 10 days or 1 month. Square root of time
scaling assumes a random diffusion process with no autocorrelation,
trending, or mean reversion. VaR, Relative VaR, Marginal VaR,
and Incremental VaR
Assuming 95 percent confidence and a 1-day horizon, a VaR of $1 million
means that, on average, only on 1 day in 20 would an institution expect to
lose more than $1 million due to market movements. This definition of
VaR uses a 5 percent risk level (95 percent confidence). On average, losses
exceeding the VaR amount would occur 5 percent of the time, or losses less
than the VaR amount of $1 million would occur 95 percent of the time.
Within a company, uncertainty in future earnings and cash flow is caused
not only by uncertainty in an institution’s underlying activity (e.g., sales
volumes), but also by a number of other risks, including market risk. Market risk can arise from a number of factors, including foreign exchange exposures, interest rate exposures, commodity price–sensitive revenues or
expenses, pension liabilities, and stock option plans. To address the institution’s need to quantify the impact of market risk factors on earnings and
cash flow, additional coefficients for volatility have been defined:
Building Blocks for Integration of Risk Categories
Earnings at risk (EaR). The maximum shortfall of earnings, relative
to a specified target, that could be expected based on the impact of
market risk factors on a specified set of exposures for a prespecified
time horizon and confidence level. Generally, earnings are reported
on a per share of equity basis. Therefore, many companies prefer to
use an earnings per share at risk (EPSaR) measure.
Cash flow at risk (CFaR). The maximum shortfall of net cash
generated, relative to a specified target, that could be expected
based on the impact of market risk factors on a specified set of
exposures for a specified time horizon and confidence level.
To better understand and interpret VaR, it is important to keep in
mind that VaR is a flexible risk measurement in different dimensions:
VaR can be defined for various horizons and confidence levels.
VaR can be expressed as a percentage of market value or in
absolute currency terms.
Apart from the normal VaR, there are three related VaR measures:
1. Relative VaR. The relative VaR coefficient expresses the risk of
underperformance relative to a predefined benchmark, such as
an index, a portfolio, or another position. Relative VaR is also
commonly expressed as a percentage of present value.
2. Marginal VaR. The marginal VaR coefficient expresses how the
removal of an entire specific position changes the risk of a portfolio. Marginal VaR can be computed for both absolute VaR and relative VaR. Marginal VaR is useful for identifying which position
or risk category factor is the largest contributor to portfolio risk.
3. Incremental VaR. Marginal VaR measures the difference in portfolio risk caused by removing an entire position, whereas incremental VaR measures the impact of gradual small changes in
position weighting. The overall sum of all incremental VaR adds
up to the total diversified portfolio VaR. Therefore, incremental
VaR may be used to calculate percentage contribution to risk.
One of the most useful applications of incremental VaR is in reporting the rank contribution to risk-hedging opportunities. Incremental VaR is also useful for identifying positions for gradual
risk reduction using partial hedges.
Market risk models are designed to measure potential losses due to adverse changes in the value of financial instruments. There are several ap-
proaches to forecasting market risk, and no single method is best for every
situation. Over the last years, VaR models have been developed and implemented throughout the financial sector and by nonfinancial institutions as well. Having roots in modern portfolio theory, VaR models
forecast risk by analyzing historical patterns of market variables. Over
time, three main methods have evolved and become established: parametric analysis, historical simulation, and Monte Carlo simulation. To understand the strengths and weaknesses of the different methods, it is
important to discuss the nature and impact of linear and nonlinear instruments. A financial instrument is regarded as nonlinear if its price (and
thus its value) changes disproportionately relative to the price changes in
the underlying asset. The risk of nonlinear instruments (e.g., options and
structured products) is more complex to estimate than the risk of linear instruments (e.g., traditional stocks, bonds, swaps, forwards, and futures).
To account for the discontinuous payoff of nonlinear instruments such as
options, risk simulations should use full valuation formulas (e.g., BlackScholes) rather than derived first-order sensitivities (e.g., delta). Table 5-8
describes the three main methodologies for calculating VaR.
Monte Carlo and historical simulations are mechanically somewhat
similar, as they both revalue instruments given changes in market rates
(scenarios). The difference lies in how the scenarios are defined. Monte
Carlo simulation generates random hypothetical scenarios using a random generator, while historical simulation estimates parameters from actual past market movements as scenarios. From a practical perspective,
the important impact of the methodology choice is that a portfolio/position with significant nonlinear exposures, and a simulation approach
(Monte Carlo or historical) with full position revaluation, will estimate the
loss distribution conceptually with more accuracy than a parametric approximation for estimating VaR. Table 5-8 summarizes the advantages
and disadvantages of each methodology. All three approaches for estimating VaR have something to offer and can be used together to provide a
more robust estimate of VaR.
The choice of a methodology has some far-reaching impacts. The model’s
user should not view models as black boxes that produce magic numbers.
It’s important to realize that all three methodologies for measuring VaR
are limited by a fundamental assumption that future risk can be predicted
from the historical distribution of returns. The parametric approach assumes normally distributed returns, which implies that parametric VaR is
only meant to describe losses on a “normal” day. Other types of days, such
as crises (fat-tail events), which happen rarely but have a serious impact,
do not exist within the “normal” view. While Monte Carlo simulation of-
Accurate* for all instruments.
Provides a full distribution of potential portfolio values (not just a
specific percentile).
Permits use of various distributional assumptions (normal, Tdistribution, normal mixture, etc.), and therefore has potential to
address the issue of fat tails (formally known as leptokurtosis).
No need for extensive historical data.
No assumption on linearity, distribution, correlation, and
volatilities required.
Accurate* for all instruments.
Provides a full distribution of potential portfolio values (not just a
specific percentile).
No need to make distributional assumptions (although parameter fitting may be performed on the resulting distribution).
Faster than Monte Carlo simulation because fewer scenarios
are used.
Estimates VaR by regenerating history; requires actual historical
rates and revalues positions for each change in the market.
Monte Carlo
*If used with complete pricing algorithm.
Fast and simple calculation.
No need for extensive historical data (only volatility and
correlation matrix are required).
Estimates VaR with an equation that specifies parameters such
as volatility, correlation, delta, and gamma.
Requires a significant amount of daily rate history (note, however,
that sampling far back may be a problem when data is irrelevant
to current conditions, e.g., currencies that have already devalued).
Difficult to scale far into the future (long horizons).
Coarse at high confidence levels (e.g., 99% and beyond)
Somewhat computationally intensive and time consuming
(involves re-valuing the portfolio under each scenario, although
far fewer scenarios are required than for Monte Carlo)
Incorporates tail risk only if historical data set includes tail events.
Pricing models required, increasing complexity.
Less accurate for nonlinear portfolios, or for skewed distributions.
Accurate for traditional assets and linear derivatives; less
accurate for nonlinear derivatives.
Historical correlation and volatilities can be misleading under
specific market conditions.
Cash flow mapping required.
Computationally intensive and time consuming (involves
revaluing the portfolio under each scenario).
Quantifies fat-tailed risk only if market scenarios are generated
from the appropriate distributions.
Appropriate for all types of instruments, linear and nonlinear.
Summary of Advantages and Disadvantages of Alternative Methodologies of Calculating VaR
T A B L E 5-8
fers a way to address the fat-tail problem by allowing a variety of distributional assumptions, volatility and correlation forecasts are still based on
statistical fitting of historical returns. While historical simulation performs
no statistical fitting, it implicitly assumes that the exact distribution of past
returns forecasts future returns distributions. This means that all three approaches are vulnerable to structural changes or sudden changes in market behavior. Stress testing is required to explore potential regime shifts to
best complement VaR and to review the accuracy of the VaR assumptions.
5.6.1 Parameters for VaR Analysis
Before calculating VaR, we need to specify three parameters: confidence
level, forecast horizon, and base currency. Confidence Level
The first step is to determine a confidence level or probability of loss associated with VaR measurement. Confidence levels generally range between
90 and 99 percent. Generally, a 95 percent confidence level as a baseline is
common in the market. Instead of fixing only a single parameter, some institutions use several confidence levels (e.g., 95 percent and 99 percent)
and forecast periods (e.g., one day, one week, and one year). It can be argued that using implied volatilities links risk prediction to market expectations as opposed to past market movements, and thus is forward looking.
For a portfolio view of risk, however, historical correlations of market returns must still be applied, as it is generally impossible to get such information from option prices, especially for OTC-traded instruments.
Determining Confidence Levels
In choosing confidence levels for market risk, the institution should consider worst-case loss amounts that are large enough to be substantial, but
that occur frequently enough to be observable. For example, with a 95 percent confidence level, potential losses should exceed VaR about once a
month on average (or once in 20 trading days), giving this risk statistic a
visceral meaning. Using a higher level of confidence, such as 99.9 percent,
is generally regarded as more conservative. But one might also reason that
a higher confidence level might mistakenly lead to a false sense of security. A 99.9 percent VaR will not be understood as thoroughly or taken as
seriously by risk takers and managers because losses will rarely exceed
that level, as a loss of that magnitude is expected to occur about once in
four years. Due to fat-tailed market return distributions, a high confidence
level VaR is difficult to model and verify statistically. VaR models tend to
lose accuracy beyond the 95 percent mark and even more beyond 99 percent. When using VaR for measuring credit risk and capital, however, a 99
percent or higher confidence level VaR should be applied because of the
Building Blocks for Integration of Risk Categories
likelihood of low-probability, event-driven risks (i.e., tail risk). Beyond a
certain confidence level, rigorous stress testing becomes more important
than statistical analysis. Forecast Horizon
Generally, active financial institutions (e.g., investment banks, hedge
funds) consistently use a one-day forecast horizon for their VaR analysis
of all market risk–driven positions. For banks, it simply doesn’t make
sense to project market risks much further because trading positions can
change dynamically from one day to the next. On the other hand, investment managers often use a one-month forecast horizon, while corporations may apply quarterly or even annual projections of risk for their
financial positions.
Applying Longer Horizon for Illiquid Assets
Instead of applying a single horizon, some institutions apply different
forecast horizons across asset classes to account for liquidity risk. It can be
argued that the unwind period for an illiquid emerging market asset is
much longer than for a government bond, and therefore a longer horizon
(e.g., one week) for emerging markets should be used. However, a better
solution is to treat market risk and liquidity risk as separate issues. Liquidity risk is currently a hot research topic, and new quantitative
methodologies are being developed.15
Simply using a longer time horizon for illiquid assets is not adequate,
and confuses liquidity risk with market risk in an overly simply manner
that is not appropriate in relation to the complexity of this topic. A standard
horizon for VaR across asset classes facilitates the risk communication
process and allows comparison for market risk across asset classes. Confidence Level Scaling Factors
Using a parametric approach, standard deviations can be used to estimate
lower-tail probabilities of loss. Lower-tail probability of loss refers to the
chance of loss exceeding a prespecified amount. Because returns tend to
cluster around the mean, larger standard deviation movements have a
lower probability of occurring. To arrive at the tail probability of loss levels and implied VaR confidence levels, standard deviations (confidence
level scaling factors) are used. Figure 5-3 shows three confidence level
scaling factors and their associated levels of tail probability of loss.
Assuming normality, one confidence level can be easily converted to
a two-standard confidence level. For example, a 95 percent confidence
level VaR is translated to the BIS standard of 99 percent confidence level
through a simple multiplication, as shown in Table 5-9.
The confidence level transformation is based on the critical assumption of a normal distribution. As will be discussed later, the assumption of
F I G U R E 5-3
Confidence Level Scaling Factors.
1.28 (90% confidence level)
1.65 (95% confidence level)
2.33 (99% confidence level)
Unexpected event at
99th percentile level
normal distribution is not supported by empirical evidence over time and
depends as well on the asset class the distribution is calculated for. Regulators are increasingly discouraging this simple conversion, as the assumption of normally distributed P&Ls is often an oversimplification,
especially when portfolios contain nonlinear positions. Base Currency
The base currency for calculating VaR is typically the currency of the equity capital and reporting currency of a company. For example, Goldman,
Sachs & Co. would use U.S. dollars to calculate and report its worldwide
risks, while the Credit Suisse Group would use Swiss francs.
T A B L E 5-9
Confidence Level Transformation from RiskMetrics Approach to BIS Standard
Confidence Level
Confidence Level
Scaling Factor
RiskMetrics VaR
95% to 99%
RiskMetrics VaR × 2.33/1.65
VaR Methodology
Converting RiskMetrics to BIS
Building Blocks for Integration of Risk Categories
371 Time Scaling of Volatility
Risk increases with time: the longer a position is held, the greater the potential for loss. But, unlike expected returns, volatility does not increase linearly
with time. Long-horizon forecasting is complicated due to mean reversion
of market returns, autocorrelation, trending, and the interrelationship of
many macroeconomic factors. Autocorrelation refers to correlation between
successive days’ returns; mean reversion is the tendency for time series to
revert to a long-term average (this is observed especially for interest rates).
VaR estimates have to be time scaled (for example, when converting a daily
VaR to a 10-day-horizon regulatory VaR standard). A commonly applied
method is square root of time scaling, which (approximately) extrapolates
one-day volatilities as well as one-day VaR to longer horizons. This method
assumes that daily price changes are independent of each other and that
there is no mean reversion, trending, or auto-correlation in the markets. To
scale volatility, time the number of trading days as opposed to actual days (5
trading days per week, 21 days per month). For example:
Weekly volatility = 1-day VaR ⋅ 兹5苶
= 1-day VaR ⋅ 2.24
Monthly VaR = 1-day VaR ⋅ 兹21
= 1-day VaR ⋅ 4.58
The simplified time-scaling approach can be useful for converting
one-day management VaR figures to 10-day figures, for example for BIS
regulatory VaR standards. However, regulators are not supportive of this
approach, which has prompted some institutions to adopt more accurate
methodologies. Time Horizon and Credit Risk
Much of the academic analysis and industry rating data is expressed on an
annual basis. This is a convention rather than an empirically supported
fact. It is important to note that there is nothing about the credit risk
methodology that supports a one-year horizon per se. Indeed, it is difficult
to support the argument than any one particular risk horizon is best. Illiquidity, credit relationships, credit deterioration, and common lack of
credit hedging instruments can all lead to prolonged risk-mitigating actions. The choice of risk horizon raises two practical questions:
1. Should credit risk be calculated for only one risk horizon or for
longer or shorter periods?
2. Is there any empirical evidence that any one particular horizon
is best?
Should there be one horizon or many? The choice of time horizon for
risk measurement and risk management is not clear because there is no explicit theory to guide us. Many different security types bear credit risk.
One of the common arguments in favor of multiple credit risk horizons is
that they allow us to calculate risk at horizons tailored to each credit security type. For instance, it may be that interest rate swaps are more liquid
than loans. The managers for each security type (e.g., loans versus swaps)
may wish to see their security type calculated at their own risk horizon.
However, the risk estimates for these different subportfolios cannot be aggregated if there is a mismatch in time horizons. Additionally, the periodic
disclosure statements required for all listed companies (generally quarterly) and annual fiscal and business reporting disclose credit information
on a quarterly/annual basis, unlike market prices for listed companies,
which are listed daily.
What is a good risk horizon? Almost any risk measurement system
is better at stating relative risk than absolute risk. Since relative risk measurements will likely drive investment decisions, the choice of risk horizon is not likely to make an appreciable difference. The key element of any
risk measurement system is the resulting risk-mitigating actions of the underlying positions, as any given risk horizon is likely to lead to the same
qualitative decisions. Although these actions may differ among institutions, the risk horizon is not likely to be significantly less than one quarter
for a bank with loans, commitments, financial letters of credit, etc. On the
other hand, the natural turnover due to ongoing maturity and reinvestment of positions provides appreciable room for risk-mitigating action
even for highly illiquid instruments. Thus, using as a convention a oneyear risk horizon—not unlike the convention for annualized interest
rates—is common, at least for reporting purposes. Even if risk-mitigating
actions are performed daily, recalculating risk at a longer horizon can still
provide guidance on changes in relative risk.
Two credit risk modeling parameters must reflect the different risk
1. The transition from one risk horizon to another must be reflected in the formulas used to reevaluate all parameters influenced by or linked to alternating risk horizons.
2. The likelihood of credit quality migration, as shown in the transition matrix, must incorporate the new risk horizon in order to
reevaluate the transition matrix for the new risk horizon, including all linked parameters.
One way of doing the latter is simply to multiply the short-horizon
transition matrices to obtain the transition matrix for a longer horizon. For
example, a two-year transition matrix could be obtained by multiplying
the one-year transition matrix by itself. However, this methodology unfor-
Building Blocks for Integration of Risk Categories
tunately ignores the impact of autocorrelation on the credit quality changes
over multiple time horizons. A nonzero autocorrelation would indicate
that successive credit quality movements from one rating bucket to another
are not statistically independent between adjoining periods. The impact of
autocorrelation is relevant for market risk calculations as well. For instance, some markets tend to exhibit mean reversion (that is, a tendency for
prices to return to some stable long-term level). Autocorrelation prevents
us from directly translating daily volatilities to monthly or yearly volatilities in a simple way. Regrettably, the issue of time period interdependencies can also arise for credit quality migrations.17 The issues surrounding
transition matrices are discussed in more detail in Sections 3.5 to 3.8.
Different Approaches to Measuring VaR Delta-Normal Method
Calculating VaR for a single position is relatively simple. However, questions arise as VaR must be measured for large portfolios with complex positions that evolve over time. The portfolio return can be written as:
R p,t + 1 = 冱 wi,t ⋅ R i,t + 1
where the weights wi,t are indexed by time to emphasize the dynamic nature of trading positions.
The delta-normal approach assumes that all asset returns are normally distributed. As the portfolio is a combination of the assumed normal distributed positions, the portfolio return is a linear combination of
normal variables and thus also normally distributed. Using matrix notations, the variance of a portfolio can be written as:
V(R p,t + 1) = w1t ⋅ 冱 wi,t ⋅ R i,t + 1
Written in this form, risk is generated by a combination of linear exposures to the factors that are assumed to be normally distributed and by
the forecast of the covariance matrix 冱t + 1. This approach supposes a local
approximation to price movements. The covariance can be generated by
two methods. First, it can be measured solely based on historical data. The
alternative approach is to apply risk measures from options to the measurement of the covariance matrix, or a combination of both methods.
The advantages of the delta-normal method are that:
It can be applied to a large number of assets and is simple to
The assumption of normal distributed asset returns is true for a
large number of frequently traded positions in a liquid market.
The criticisms of the delta-normal method are that:
The option-implied measures of risk are superior to historical
data, but are not available for every asset position.
This approach accounts inadequately for event risk. The normal
distribution based on historical data does not represent
infrequent and extreme events by the structure of the probability
distribution per se. This is a general and structural shortcoming
of all methods relying on historical data.
Fat tail distribution is a common problem in the measurement of
the distribution of returns on most financial assets. As VaR attempts
to measure the behavior of the portfolio return on the left tail, fat
tails are particularly worrisome. In a model based on normal
distributed returns but with fat tails in the position or portfolio
return distribution, the normal approximation underestimates the
proportion of outliers and thus the true value of risk.
The delta-normal approach reflects nonlinear exposures inadequately. Option positions are represented by their deltas to the underlying
asset. With an at-the-money call, ∆ = 0.5 and a long position in the option
is replaced by a 50 percent position in the underlying asset. Unfortunately,
however, changes in the values of option positions depend on changes in
underlying spot rates but also on the level of the spot rates. At-the-money
options display high convexity, which generates unstable deltas. The linear approximation to nonlinear positions is valid for only a very narrow
range of underlying spot prices. Delta Versus Full Valuation
The assumption of normal distribution is particularly convenient because
of the invariance property of normal distributed variables; thus portfolios
of normal distributed variables are themselves normally distributed. As
mentioned earlier, because portfolios are linear combinations of specific
positions, the delta-normal approach is fundamentally linear.
Because utilizing the Black-Scholes formula can be computationally
intensive, particularly when there is a large number of scenarios and securities, it is often desirable to use a simple approximation of the formula.
The simplest such approximation is to estimate changes in the option
value via a linear mode, which is commonly known as the delta approximation. In this case, the initial value V0 and a price change from P0 to P1 results in:
V1 = V0 + δ(P1 − P0)
Building Blocks for Integration of Risk Categories
δ = ᎏ V(P,S,τ)|P0
The potential loss in value V is thus defined as:
∆V = β0 ⋅ ∆S
where β0 is the portfolio sensitivity to change in prices
V0 is the current position
∆S is the potential change in prices
The normality assumption allows the calculation of the portfolio beta
as the (weighted) average of the individual betas. A fundamental advantage of this approach is that it requires the measurement of the portfolio
only once at the current position V0, which is directly linked to the current
prices S0. The delta-normal approach applies to portfolios that are exposed
to many different risk factors, such as equity, interest and fx factors, as the
computation is simple and straightforward. However, the delta-normal approach does not fit well with a portfolio with options because:
The portfolio delta can change very fast (given high gamma
The portfolio delta may be asymmetric for up and down moves.
The worst loss may not be reflected for two extreme realizations
of the spot rate of the underlying asset.
The latter problem is clarified by this example: a portfolio consists of
a call and a put on the same underlying asset. The worst payoff possible
(the sum of the premiums) will be realized if the underlying spot rate does
not move. It is not enough to measure the portfolio at the two extremes.
All intermediate values must be verified and measured as well.
The full valuation approach, in contrast to the delta-normal valuation, requires the computation of the values of the portfolio for different
levels of prices:
∆V = V(S1) − V(S0)
Although this approach is theoretically more correct, it has the drawback of being quite computationally demanding. It requires marking to
market the complete portfolio over a large number of realizations (prices)
of underlying random variables (equity prices, interest rates, etc.). Full
valuation must be performed to measure the risk option trading books exposed to a limited and well-known number of risk factors.
The difference between the results of linear and nonlinear exposures is illustrated in Figures 5-4 and 5-5. In both cases, the underlying
market factor is assumed to follow a normal distribution. In Figure 5-4,
the payoff is a linear function of the underlying price and is displayed in
the upper left graph. The price of the underlying asset is normally distributed as shown in the upper right graph. As a result of the linear function, the profit itself is normally distributed, as shown at the bottom of
the figure. The VaR of the P&L can be found from the exposure and the
VaR for the underlying price. There is one-to-one mapping between the
two VaR measures.
Figure 5-5 displays the profit function for an option, which is nonlinear. (See the case study of Barings in Section 6.5, where Nick Leeson
used straddles and failed, and his market assumptions and the complexity of the instrument worked against him.) The resulting profit distribution is skewed to the left. The VaR of the portfolio and the underlying asset
cannot be directly linked, as there is a nonlinear relation.
F I G U R E 5-4
Distribution with Linear Exposures.
Spot price
Spot price
Building Blocks for Integration of Risk Categories
F I G U R E 5-5
Distribution with Nonlinear Exposures.
Spot price
Spot price
Profit Delta-Gamma Method
The main drawback of the delta-normal method is that all risk parameters
except the delta coefficient are lost. The elegance of the standardized application on different risk factors and among large portfolios is that it is
given a simplification that strips away all nonlinear components. The Taylor expansion contains gamma and theta risks, which can be added to capture the nonlinear risk components (the expansion can also include vega
risk to reflect exposures in volatility changes; however, this has been
dropped in this example for simplicity).
V1 = V0 + δ(P1 − P0) + ᎏ Γ(P1 − P0)2
V1 = V0 + δ(P1 − P0) + ᎏ Γ(P1 − P0)2 − θt
where t is the length of the forecast horizon and δ, Γ, and θ are net values
for the total portfolio including options, which are all written on the same
underlying instrument18 and are defined by:
Γ = ᎏ2 V(P,S,τ)|P0
θ = ᎏ V(P,S,τ)|τ0
Figure 5-6 shows the delta, delta and gamma, and full valuation for
an option. As can be seen, the delta-gamma-theta approximation almost
perfectly duplicates the full valuation case.
Using a delta-normal approach, VaR is written as:
VaR1 = |δ|(ασS)
where α is a function of the selected confidence level.
F I G U R E 5-6
Delta-Gamma-Theta Approximation versus Full and Delta Approximation.
Full valuation
Delta-gamma approach
Delta-normal approach
– 0.01
Building Blocks for Integration of Risk Categories
Using higher-order terms, VaR can be written as:
VaR1 = |δ|(ασS) − ᎏ Γ(ασS)2 − |θ| |Sdσ|
A negative Γ represents a net short position in options, which results
in an add-on for the second term; otherwise the second term will decrease
the total VaR. The third term θ represents an add-on to VaR due to exposures in changes in the time to maturity. Given a net long position with a
negative θ, dσ leads to a positive change (increase) in time at the α confidence level; otherwise, for a net short position with a positive θ, dσ leads
to a decreasing volatility at the α confidence level.
Moving away from linearity, the calculation of the distribution of
changes in the portfolio value V becomes complex and cannot be directly
linked to the VaR of the underlying position or portfolio.
The delta-gamma approach can be applied to many sources of risk.
One approach to finding the portfolio VaR is the simulation of the movements in the market prices dS. Using a simulation technique, a large realization can be derived from the distribution
dS ≈ N(0,Σ)
where Σ represents the covariance matrix of changes in prices.
The delta-gamma approach is unfortunately not very practical because, as it requires many sources of risk, the required amount of data increases geometrically. For example, for a portfolio with N = 100, 100
estimates are required of δ, 5050 estimates for the covariance matrix Σ, and
an additional 5050 estimates for the matrix Γ, including the second derivatives of each position within the portfolio with respect to each source of
risk. Thus, for such a portfolio, a full Monte Carlo simulation approach
provides a more efficient and effective VaR measurement. Comparison of Delta Versus Full Valuation
Each of the discussed methods is best adapted to a different application:
The delta-normal approach fits best with large portfolios where
optionality is not a dominant component.
The delta-gamma approach fits best with portfolios with limited
exposures to risk factors and with a dominant optionality
component, as it provides superior precision with reasonable
computational requirements.
The full valuation or Monte Carlo simulation approaches fit best
with portfolios with substantial components of optionality and
exposures to several risk factors.
The discussion of the linear/nonlinear component has direct implications for the selection of the time horizon. With linear approaches, VaR
can be easily adjusted to other periods by simply scaling a square root of
time factor. These time horizon adjustments are based on the assumption
that the position is constant and that all (daily) returns are independent
and identically distributed. These time horizon adjustments are not applicable for positions with substantial components of optionality. As derivative instruments can be replicated by dynamically changing positions in
the underlying assets, the risk of the derivative instruments can be dramatically different from the scaled measure of daily risk. Thus, time horizon adjustments of daily volatility to longer time horizons using the
square root of the time scaling factor are valid only when positions are
constant and when optionality in the portfolio is negligible. The full valuation or Monte Carlo simulation approach must be applied for portfolios
or positions with substantial optionality components over the required
time horizon, instead of scaling a daily VaR measure.
Historical Simulation Method
The historical simulation method can be viewed as a straightforward implementation of the full valuation method. By going back in time—say, for
250 days—and applying current weights to a time series of historical asset
returns, the history of a hypothetical portfolio using the current position is
Rp,τ = 冱 wi,t ⋅ Ri,τ
τ = 1, . . . , t
The weights wt are kept at their current values, not the historical values. The full valuation requires a set of complete prices, such as yield
curves. Hypothetical future prices for scenario τ are derived from applying historical price movements to the current level of prices:
P*i,τ = P*i,0 + ∆Pi,τ
i = 1, . . . , N
A new portfolio value P*p,τ is calculated from the full set of hypothetical
prices, including nonlinear optionality components. In order to capture
vega risks, the set of prices used can incorporate implied volatility measures
to accommodate the option’s price change relative to changes in volatility.
This generates the hypothetical return corresponding to observation τ:
P*p,τ − Pp,0
Rp,τ = ᎏ
Building Blocks for Integration of Risk Categories
VaR is then calculated from the entire distribution of hypothetical returns. This method is relatively straightforward to implement if historical
data has been collected over a certain time period. The choice of the length
of the sample period reflects the trade-off between longer and shorter
sample sizes. Longer time periods increase the accuracy of the estimates;
in contrast, the estimate based on a shorter time frame might be irrelevant
due to missing important changes in the underlying data caused by shortterm structural changes.
This method considers the selection of time horizon for measuring
VaR as the returns are calculated simply over intervals that correspond to
the length of the VaR time horizon. For example, to calculate a monthly
VaR, historical monthly portfolio returns are calculated over the last five
Being based on actual prices, this method is independent regarding
nonlinearities and nonnormal distribution and thus captures gamma,
vega risk, and correlations. The full valuation is based in its simplest
form on historical data. The approach does not depend on assumptions
and conditions about valuation models or the underlying stochastic
structure of the instruments. It considers fat tails and is not prone to
model risk.
However, the historical simulation method is subject to a number of
criticisms. The most critical assumption of the historical simulation
method is that the past foretells the future. Another issue is that risk contains significant and predictable time variation. The historical simulation
approach tends to overestimate the meaningfulness of historical data for
the future and to miss situations with temporarily elevated volatilities or
structural changes.
The quality of VaR measures calculated with the historical simulation method is linked to the length of the historical period, with the same
advantages and disadvantages discussed earlier. Another debated issue is
the moving average estimation of variances. The historical simulation
method allocates the same weight to all observations over the length of the
time horizon. As the observation period can include data from structural
changes, and short-term elevated volatilities, the measure of risk can
change significantly after an old observation is excluded from the time
The last critical issue relates to large portfolios with complex instruments, which require extensive databases and computational power. A
simplification used in practice is the bucketing approach, where cash
flows are allocated into time bands, such as interest rate payoffs, dividends, etc. This increases the speed of computation and is accepted and
adopted by the regulators. If the bucketing approach is used with too
many simplifications, the benefits of full valuation can be lost due to lowered accuracy and precision of the VaR information received.
5.6.4 Stress Testing
Stress testing is completely different from historical or Monte Carlo simulation. Stress tests, sometimes called scenario analyses, are designed to estimate potential economic losses in abnormal markets to examine the effect
on key financial variables on the portfolio. Historical analysis of markets
shows that returns have fat tails, where extreme market moves (i.e., beyond 99 percent confidence) occur far more frequently than a normal distribution would suggest. Although risk management as a practice has
improved considerably, events such as natural disasters, wars, and political coups still lie beyond statistical forecasting. For instance, a scenario
where the yield curve moves up by 100 basis points over a month, or
where a currency is suddently devalued by 20 percent, can be specified.
Regular stress testing is increasingly viewed as indispensable by risk
managers and regulators. Stress tests should enhance transparency by exploring a range of potential low-probability events when VaR bands are
dramatically exceeded. Stress testing combined with VaR gives a more
comprehensive picture of risk. Such scenarios are well known within the
traditional asset liability management (ALM) approach.
The usefulness of such an approach depends on whether such scenarios adequately represent typical market moves. Stress testing should
answer two central questions:
1. How much is the loss if a stress scenario occurs, e.g., if the U.S.
equity market crashes by 20 percent?
2. What event or risk factor could cause an institution to lose more
than a predefined threshold amount, e.g., $1 million?
The first issue is commonly covered by a top-down approach for
stress testing. Senior management or regulators want to be informed
about how much the firm may lose in a major equity market crash. The
second issue is usually raised in a bottom-up environment, such as at the
book or business level. After scenarios are collected from individual risk
takers, their potential losses can be measured and aggregated over the different exposures of the risk takers. For example, a stress scenario of depreciation of Euros vs. U.S. dollars might be ruled unimportant due to
generally offsetting sensitivities (or nonmaterial reported sensitivities),
while a scenario of widening credit spreads (e.g., lower ratings) could
be identified as relevant. This approach could therefore be viewed as a
bottom-up search for relevant stress scenarios. How to Use Stress Tests
The key issue with stress tests is how to create and use them. To be meaningful, stress tests should tie back into the decision-making process.
Corporate-level stress test results should be discussed in a regular forum
Building Blocks for Integration of Risk Categories
by risk monitors, senior management, and risk takers. Just as for VaR limits, companies should have a set of stress loss limits categorized by risk
type and risk-taking unit.
Stress testing should be performed at multiple levels of the micro,
macro, and strategic risk pyramid at different frequencies. At a senior
management level, stress results should guide the firm’s appetite for aggregate risk taking and influence the internal capital allocation process. At
the book level, stress tests may trigger discussions on how best to unwind
or hedge a position. Development of Stress Test Parameters
The goal of stress testing is to uncover potential concentration risks and
make them more transparent. Good stress tests should therefore:
Be relevant to current exposures. A concentrated portfolio with
large risks may incur substantial losses from relatively small
movements in certain risk factors.
Consider changes in all relevant risk factors. Stress scenarios should
consider all potential changes in a complete set of risk factors. A
stress scenario in isolation does not reflect reality, as risk factors
don’t move in isolation (especially when they are extreme).
Examine potential structural changes. A key question in
developing a stress scenario is whether current risk parameters
will hold or break down under extreme conditions. It is key to
know if observed correlations hold or increase, or to what extent
a structural change (i.e., decoupling of risk factors) could occur.
For example, during large equity shocks (e.g., the 1987 crash and
the 1997 and 1998 sell-offs), a flight to safety often results in a
reversal of the normally highly positive correlation between
stocks and government bonds: as stocks plummet, bonds rise
because investors move into safer and more liquid assets. In the
market turmoil of September 1998, LTCM experienced this
problem when credit spreads widened and interest rates fell due
to a flight to safety.
Consider market illiquidity. Stressed markets are often
characterized by material loss of liquidity. Liquidity can be
viewed from two perspectives: the ability to trade positions
without moving the prices and the ability to fund positions. For
example, Brazilian bond traders reported that bid-ask spreads
were so wide during the October 1997 liquidity crisis that it was
unclear whether the local yield curve was upward or downward
sloping. As prices in the marketplace cease to exist, it becomes
impossible to mark positions to market. The threat of liquidity
risk motivated the recapitalization of LTCM by a consortium of
14 commercial and investment banks in September 1998. In a
statement to the U.S. House of Representatives, Federal Reserve
Chairman Alan Greenspan stated that “the consequences of a
fire sale triggered by cross-default clauses, should LTCM fail on
some of its obligations, risked a severe drying up of market
Consider the interplay of market and credit risk. Stressed markets
often give rise to counterparty exposures that may be much more
significant than pure market impacts. While market rates and
creditworthiness are unrelated for small market moves, large
market movements could precipitate credit events, and vice
versa. A market-neutral risk arbitrage book would consist of a
series of long and short positions, which hedges out market risk
but is exposed to firm-specific risk. A trading strategy that
eliminates broad market risk (equity, interest rates, foreign
exchanges, or commodities) leaves only residual risk. For
example, a hedge fund manager can hedge the market risk of a
U.S. stock portfolio by shorting S&P 500 Index futures, leaving
only firm-specific residual risk. Forecasting Time Frame
The forecast time horizon for the stress scenario should reflect the institution’s typical holding period. Banks, brokers, and hedge funds tend to
look at one-day to one-week worst-case forecasts, while longer-term investors, such as mutual and pension funds, may view a one-month to
three-month time frame as adequate. Corporations may use up to an annual horizon for strategic scenario analysis.
Steps for Stress Testing
There are three basic steps for stress testing:
1. Generate scenarios. The most challenging aspect of stress testing
is generating credible worst-case forecasts that are relevant to
portfolio positions. Scenarios should address both the magnitude of movement of individual market variables and the interrelationship of variables (i.e., correlation or causality).
2. Revaluate the portfolio/positions. Revaluing a portfolio or position involves marking to market all financial instruments under
new worst-case market rates. Stress test results are generally
changes in present value, not VaR.
3. Aggregate results. The results have to be aggregated to show expected levels of mark-to-market losses or gains for each stress
scenario and in which entity the losses or gains are concentrated.
Building Blocks for Integration of Risk Categories
Creating Stress Scenarios
There are a variety of approaches to generating stress tests, such as:
The predictive scenario generation, in which a subset of stressed
risk factors is used with historical volatilities or correlations to
predict the moves of all other market variables.
A natural approach, in which scenarios are based on historical
periods with extreme market conditions (see Table 5-10). Some
infamous events include the 1987 U.S. stock market crash, the
Exchange Rate Mechanism (ERM) crisis, the Fed rate hike in 1994,
the 1995 Tequila crisis, the 1997 Asian crisis, the volatile markets
in 1998, and the 1999 Brazil devaluation. In this approach, data is
captured from relevant historical stress periods and a portfolio is
valued with historical simulation to measure potential losses.
RiskMetrics research has assembled a representative global
model portfolio consisting of 60 percent equities and 40 percent
fixed-income instruments to identify pertinent time periods for
historical stress tests. Both one-day and five-day portfolio returns
were used to identify extreme loss periods.
How does the severity of loss depend on global volatility? Figure
5-7 shows the volatility of the Nasdaq index for a period that includes three
of the historical scenario dates. Obvious patterns can be seen during the
time of the Gulf War, the Asian crisis, and the TMT crisis in March/April
T A B L E 5-10
Major Loss Events of the Past 20 Years
Black Monday
Return (%)
Return (%)
Gulf War
Mexican peso fallout*
Asian crisis
Russian currency devaluations
RiskMetrics Group, Risk Management: A Practical Guide, New York: RiskMetrics Group, 1999, p. 28, reproduction
with permission of RiskMetrics Group, Inc.
*The Mexican peso was actually devalued at the end of 1994. On January 23, 1995, the peso lost 6 percent and several
Eastern European markets incurred losses of around 5 to 10 percent.
F I G U R E 5-7
Nasdaq Index Returns from July 1989 to July 2001. Data source: Bloomberg
Nasdaq index returns
–10% Evolution of Shocks from Volatility
The severity of portfolio losses appears to be related to the level of volatility in the world. For example, the Mexican peso fallout, which occurred
during a period of relative market calm when the RiskMetrics Volatility
Index (RMVI) was at an average level of approximately 100, only resulted
in a one-day return of −1 percent, while the Asian crisis and Russian devaluation, which occurred while the RMVI was significantly above 100,
resulted in more severe portfolio losses of 1.9 percent and 3.8 percent (see
Figure 5-8). This suggests that it make no sense to run the same static
stress tests in all market regimes—more volatile markets require more severe stress tests. To make stress scenarios more responsive to market conditions, the RMVI can be used as a dynamic scaling factor for stress
scenarios. The RMVI is a benchmark portfolio that measures global
volatility and is composed of equity, fixed income, and foreign exchange
markets in 28 countries, as well as three major commodity markets. Observing the daily returns of these 87 markets, RiskMetrics calculates a total
volatility across all countries and asset classes and compares it to a historical average. For more information, see Christopher Finger, RMG Volatility
Index: Technical Document, New York: RiskMetrics Group, 1998.
Building Blocks for Integration of Risk Categories
F I G U R E 5-8
Riskmetrics RMVI Methodology Applied to the Mexican Peso and U.S. Dollar from
December 1995 to March 1999. (Source: RiskMetrics Group, Risk Management:
A Practical Guide, New York: RiskMetrics Group, 1999, 28. Copyright © 1999 by
RiskMetrics Group, all rights reserved. Reproduction with permission of RiskMetrics Group, LLC.)
Mexican peso
Asian crisis
devaluations Applying Shocks to Market Factors or Correlations
A second approach to generating stress tests is to apply large shocks to either market factors or volatilities and correlations. This method can provide a good measure of the sensitivity to risk factors and can therefore be
useful in identifying trouble spots in a portfolio.
It is straightforward to alter a market rate (e.g., to lower the S&P 500
by 10 percent) or many market rates (e.g., to lower all points on the U.S.
government yield curve by 50 basis points), but the real challenge is to determine which market rates to shock and by how much. In general, these
decisions will be based on historical moves, intuition, and the characteristics of the portfolio itself. Applying Shocks to Volatilities and Correlations
VaR estimates can be stressed by applying shocks to volatilities or correlations. While volatilities can be adjusted up and down like market rates,
special care must be taken with correlation matrices because nonsensical
correlation structures can often be created from the interrelationship between factors. These correlation structures can, in turn, result in nonsensical (imaginary) VaRs.
For example, consider a three-party government. If party A and party
B always vote on opposite sides of every issue (correlation of −1), it is impossible for party C to be positively correlated with both A and B. RiskMetrics has published a methodology to adjust correlations in a mathematically
consistent fashion. The general idea is to mix an average correlation term
into a prespecified group of assets and then to adjust all diagonal terms.
This methodology is implemented in CreditManager, where it can be used
to change the average correlation among industries and countries. Anticipatory Scenarios
In generating an anticipatory scenario, a risk manager must determine the
event of interest (e.g., flight to quality within Asian markets, stock market
crash), the severity of the event (e.g., from once a year to once a decade),
and the effects of such an event on the global market. For the third determination, it is essential to move all market rates in a consistent fashion.
For example, in a flight to quality, not only will government-corporate
spreads widen, but equity prices will fall.
The next step in the stress test is to revalue the portfolio under this
scenario and to analyze sensitivities and summarize the results. Applying Portfolio-Specific Stress Tests
Another stress testing approach searches for stress scenarios by analyzing
the vulnerabilities of the specific portfolio in question. One way to discern
the vulnerabilities is by conducting a historical or Monte Carlo simulation
on a portfolio and searching for all scenarios that could cause a loss exceeding a defined threshold amount. Instead of specifying the scenario
and calculating potential losses, as in the three approaches described previously, we specify what constitutes a severe loss and search for scenarios.
5.6.5 Summary of Stress Tests
Most models make assumptions that don’t hold up in abnormal markets.
Stress tests are therefore essential for a comprehensive risk picture and
should be an integral component of risk analysis and communication.
As with VaR analysis, stress testing must be done at different levels of
the organization. The organizational hierarchy for stress testing is even
more important than for VaR reporting. At the desk level, traders are interested in stressing individual positions and specific risk factors. On a corporate level, senior management is concerned about macro stress scenarios
that could pose a threat to firmwide operations. The process of generating
and discussing stress scenarios is a collective exercise in risk analysis.
Stress tests are an opportunity to consider scenarios that most view as unlikely, but that are possible. Make stress tests workable, realistic, and
timely. Rather than stress-testing everything, focus on relevant position-
Building Blocks for Integration of Risk Categories
specific stresses. It is important for stress tests to tie into the decisionmaking process: stress test results should guide corporate risk appetite decisions, impact limits, and be a judgmental factor in capital allocation.
Stress testing can be viewed from two perspectives: what would be
the potential losses if certain events occurred, or what stress events could
lead to losses of a certain magnitude? There are four major approaches for
generating stress scenarios. The first uses historical scenarios and the second shocks market rates to examine portfolio sensitivities and concentrations. The third approach considers hypothetical future scenarios based
on current market conditions. The fourth approach searches for stress scenarios by analyzing portfolio vulnerabilities.
As discussed earlier, portfolio risk is not new to the investment industry.
Traders and merchants realized early that diversification reduces the risk
of loss. In 1959, Harry Markowitz developed an analytical framework for
portfolio analysis and looking at return and risk. The concept of portfolio
risk is not new. In order to gain better insight, the following sections focus
on the concept of VaR in the portfolio context. VaR is applied systematically to many sources of risk in the investment industry. We will mainly
apply a delta-normal approach, as this approach is a direct extension of
traditional portfolio risk analysis and is based on variances and covariances, well known from Markowitz and others.
VaR measures portfolio risk and, through decomposition in incremental VaR components, enables identification of the asset contributing
the most to the overall portfolio risk. A drawback of the linear VaR models (based on the delta-normal approach) is that the size of the covariance
matrix increases geometrically with the number of assets. Alternative approaches to reduce the size of the covariance matrix involve using diagonal and factor models.
Portfolio VaR
A portfolio p can be characterized by positions on a certain number of risk
factors. Once the structure of the decomposition is defined, the portfolio
return is a linear combination of the returns on underlying assets, where
the weights wi are given by the relative dollar amounts invested at the beginning of the period. Therefore, the VaR of a portfolio can be reconstructed from a combination of the risks of underlying securities.
The portfolio’s return from t to t + 1 is defined as:
rp,t + 1 = 冱 wi,t ⋅ ri,t + 1
where the weights wi,t are measured at the beginning of the observation
period and sum to unity of 1 (100 percent). In matrix notation, the same
portfolio return can be defined as:
rp = [w1, w2, . . . , wN] ⯗ = w′r
where w′ represents the transposed vector (i.e., horizontal) of weights and
r is the vertical vector containing individual asset returns (r1, r2, . . . , rN).
The expected value E(X) or the mean can be estimated as the weighted
sum of all possible values, each weighted by its probability of occurence:
E(X) = 冱 pi ⋅ xi
By extension of Equation (5.24), the portfolio’s expected return is defined as:
E(rp) = µp = 冱 wi ⋅ µi
and the portfolio’s variance is:
σ2p = 冱 w12σ12 + 冱 冱 wiwjσij
i=1 j=1
= 冱 w12σ12 + 2 冱 冱 wiwjσij
i=1 j<1
The variance includes the risk of the individual positions and all the
cross-products, reflected in N(N − 1)/2 different covariances.
With an increasing number of assets, it becomes difficult to generate
and manage all the different covariances on an equation basis. In matrix
notation, the variance is written as:
σ = [w1, w2, . . . , wN] ⯗
. . . σN,N
Defining cov as the covariance matrix, the portfolio variance can be
written more compactly as:
Building Blocks for Integration of Risk Categories
σ2p = w′ cov w
Using a normal distribution, the VaR measure is then ασp times the
initial investment. Lower portfolio risk can be achieved through low correlations or a large number of assets. To see the effect of N, assume that all
assets have the same risk, that all correlations are the same, and that equal
weight is put on each asset. Figure 5-9 shows how portfolio risk decreases
with the number of assets.
Start with the risk of one security, which is assumed to be 12 percent.
When p is equal to 0, the risk of a 10-asset portfolio drops to 3.8 percent; increasing N to 100 drops the risk even further to 1.2 percent. Risk tends
asymptotically to 0. More generally, portfolio risk is:
σp =
ᎏ 莦莦莦
+ 1 − ᎏ莦
N 冢
So, when p = 0.5, risk decreases rapidly from 12 percent to 8.9 percent as N goes to 10, but then converges much more slowly toward its
minimum value of 8.5 percent. Correlations are essential in lowering
portfolio risk.
F I G U R E 5-9
Number of Securities in Portfolio and Impact on Correlation (Diversification).
Correlation = 0.5
Risk (%)
Correlation = 0.0
Number of securities in portfolio
Covariances can be estimated from sample data as:
σ̂ij = ᎏ 冱 (xt,i − µ̂i)(xt,j − µ̂i)
T − 1 t=1
The covariance is a measure of the extent to which two variables
move linearly together. If two variables are independent, their covariance
is equal to 0. A positive covariance means that the two variables tend to
move in the same direction; a negative covariance means that they tend to
move in opposite directions.
The magnitude of covariance, however, depends on the variances of
the individual components and is not easily interpreted. The correlation
coefficient is a more convenient, scale-free measure of linear dependence:
ρ12 = ᎏ
The correlation coefficient ρ always lies between −1 and +1. When ρ
is equal to unity, the two variables are said to be perfectly correlated.
When ρ is 0, the variables are uncorrelated.
Correlations help to diversify portfolio risk. With two assets, the diversified portfolio variance is:
σ 2p = w12σ 21 + w22σ 22 + 2w1w2σ1ρ1,2σ2
The portfolio risk must be lower than individual risk. When the correlation is exactly unity, Equation (5.31) reduces the variance of the portfolio to
the weighted variance of the underlying positions, since the portfolio weights
sum to unity. Generally, the undiversified VaR is the sum of individual VaR
measures. Diversification into perfectly correlated assets does not pay.
So far, nothing has been said about the distribution of the portfolio return. Ultimately, we would like to translate the portfolio variance into a VaR
measure. To do so, we need to know the distribution of the portfolio return.
In the delta-normal model, all individual security returns are assumed to be
normally distributed. This is particularly convenient since the portfolio, a
linear combination of normal random variables, is then also normally distributed. At a given confidence level, the portfolio VaR is value at risk = ασp.
5.7.2 Incremental VaR
An important aspect of calculating VaR is to understand which asset, or
combination of assets, contributes most to risk. Armed with this information, users can alter positions to modify their VaR most efficiently.
Building Blocks for Integration of Risk Categories
For this purpose, individual VaRs are not sufficient. Volatility measures the uncertainty in the return of an asset taken in isolation. When this
asset belongs to a portfolio, however, what matters is the contribution to
portfolio risk.
Suppose now that an existing portfolio is made up of N-1 securities,
numbered as j = 1, . . . ,N-1. A new portfolio is obtained by adding one security, called i. The marginal contribution to risk from security i is measured by differentiating Equation (5.25) with respect to wi.
ᎏ = 2wiσ2i + 2 冱 wjσi,j
j = 1,j ≠ i
= 2 cov ri, wiri + 冱 wj rj = 2 cov (ri, rj)
We note that ∂σ2p/∂wi = 2σp∂σp/∂wi. The sensitivity of the relative
change in portfolio volatility to a change in the weight is then:
cov (ri , rj)
ᎏ = ᎏᎏ
= βi
σp ∂wi
Therefore, β measures the contribution of one security to total portfolio risk. This is also called the systematic risk of security i vis-à-vis portfolio p. Using matrix notation, β is:
cov w
w′ cov w
Beta risk is the basis for the capital asset pricing model (CAPM), developed by Sharpe (1964). According to the CAPM, well-diversified investors want to be compensated for the systematic risk of securities only.
In other words, the risk premium on all assets should depend on beta only.
Whether this is an appropriate description of capital markets has been the
subject of much of finance research over the last 20 years. Even though this
proposition is much debated, the fact remains that systematic risk is a useful statistical measure of portfolio risk.
The measure of β is particularly useful for decomposing a portfolio’s
VaR into sources of risk. We can expand the portfolio variance into:
σ2p = w1 w1σ12 + 冱 wiσ1,j
j = 1, j ≠ 1
+ w2 w2σ22 + 冱 wiσ2,j
+ ⋅⋅⋅
j = 1, j ≠ 2
This is also:
σ 2p = w1 cov (r1, rp) + w2 cov (r2, rp) + ⋅⋅⋅
= w1(β1σ 2p) + w2(β2σ 2p) + ⋅⋅⋅
冢冱 w β 冣
= σ 2p
i i
which shows that the portfolio variance can be decomposed into a sum of
components each due to asset i. Using a similar decomposition, VaR is then:
冢 冱 w β 冣 = VaR + VaR + ⋅⋅⋅
VaR = VaR
i i
Here we have decomposed the total VaR into incremental measures.
This provides vital information, as risk should be viewed in relation to the
total portfolio and not in isolation.
5.7.3 Alternative Covariance Matrix Approaches
So far, we have shown that correlations are essential driving forces behind
portfolio risk. When the number of assets is large, however, the measurement of the covariance matrix becomes increasingly difficult. With 10 assets, for instance, we need to estimate 10 × 11/2 = 55 different variance and
covariance terms. With 100 assets, this number climbs to 5500. The number of correlations increases geometrically with the number of assets. For
large portfolios, this causes real problems: the portfolio VaR may not be
positive, and correlations may be imprecisely estimated.
The following sections discuss the extent to which such problems
can affect VaR measures and propose some solutions. For many users,
however, such problems may not be relevant because they have no control
over the measurement of inputs. Until such users encounter zero VaR
measures, these sections can be safely skipped. Zero VaR Measures
The VaR measure derives from the portfolio variance, expressed as:
σ 2p = w′ cov w
In order to generate statistically useful measures, the cov has to be
positive definite. This is not always the case. The status of the cov can be
verified under two conditions:
Building Blocks for Integration of Risk Categories
1. The number of historical observations T must be greater than
the number of assets N.
2. The return time series cannot be linearly correlated.
The first condition states that if a portfolio consists of 100 assets,
there must be at least 100 historical observations to ensure that whatever
portfolio is selected, the portfolio variance will be positive. The second
condition rules out cases where an asset can be replicated exactly through
a linear combination of other assets.
An example of a non-positive-definite matrix is obtained when two
assets are identical (thus ρ = 1). In this situation, a portfolio consisting of
$1 on the first asset and −$1 on the second will have exactly zero risk.
In practice, this problem is more likely to occur with a large number
of assets that are highly correlated (such as currencies fixed to each other,
zero coupon bonds, or ADRs and the original foreign stock). In addition,
positions must be precisely matched with assets to yield zero risk. This is
most likely to occur if the weights have been optimized on the basis of the
covariance matrix itself. Such optimization is particularly dangerous because it can create positions that are very large, yet that apparently offset
each other with little total risk.
If users notice that VaR measures appear abnormally low in relation
to positions, they should check whether small changes in correlations lead
to large changes in their VaRs. Diagonal Model
A related problem is that as the number of assets increases, it is more likely
that some correlations will be erroneously measured. Some models can
help to simplify this process by providing a simpler structure for the covariance matrix. One such model is the diagonal model, originally proposed by Sharpe in the context of stock portfolios. This model is often
referred to as the CAPM, which is not correct. The diagonal (one-factor)
model is only a simplification of the covariance matrix and says nothing
about the nature of expected returns, whose description through the relationship to the market factor is the essence of the CAPM.
The assumption is that the common movement in all assets is due to
one common factor only, the market. Formally, the model is:
ri = α i + β i rm + ε i
E(εi) = 0
E(εi ,εj) = 0 E(ε 2i ) = σ 2ε,i
E(ε i rm) = 0
The return on asset i is driven by the market return R and an idiosyncratic term εi, which is not correlated with the market or across assets.
As a result, the variance can be broken down as:
σ 2i = β 2i σ 2m + σ 2ε,i
The covariance between two assets is:
σ 2i = βiβ j σ 2m
which is solely due to the common factor. The full covariance matrix is:
Cov = ⯗ [β1 . . . βN]σ 2m ⯗
. . . σ2ε,N
Written in matrix notation, the covariance matrix is:
Cov = ββ′σ 2m + Dε
As the matrix D is diagonal, the number of parameters is reduced
from N × (N + 1)/2 to 2N + 1(N for the betas, N in D and one for 0 − m).
With 100 assets, for instance, the number is reduced from 5500 to 201, a
considerable improvement regarding equation complexity and calculation time. Furthermore, the variance of large, well-diversified portfolios is
simplified even further, reflecting only exposure to the common factor.
The variance of the portfolio is:
VaR(rp) = VaR(w′r) = w′ cov w = (w′ββ′w)σ 2m + w′Dεw
The second term consists of
But this term becomes very small as the number of securities in the portfolio increases. For instance, if all the residual variances are identical and
have equal weights, this second term is
冤冱 (1/N) 冥σ
which converges to 0 as N increases. Therefore, the variance of the portfolio converges to:
VaR(rp) → (w′ββ′w)σ2m
which depends on one factor only. This approximation is particularly useful when assessing the VaR of a portfolio consisting of many stocks. It has
Building Blocks for Integration of Risk Categories
been adopted by the Basel Committee to reflect the market risk of welldiversified portfolios.
The actual correlations are all positive, as are those under the diagonal model. Although the diagonal model matrix resembles the original covariance matrix, the approximation is not perfect. The diagonal model
measures risk in relation to the market, and thus the correlation is driven
by exposure to the market and is different (usually lower) than the true correlation. This is because the market is the only source of common variation.
Whether this model produces acceptable approximations depends on the
purpose at hand. Despite the drawback of limitation in the explanatory
power of the model given only one source of common variation, there is no
question that the diagonal model provides a considerable simplification. Factor Models
If a one-factor model is not sufficient, better precision and more statistical
stability can be obtained with multiple-factor models. Equation (5.46) can
be generalized to K factors:
ri = αi + βi,1ri + . . . + βi,k rk + εi
where r1, . . . , rk are factors independent of each other. In the previous
three-stock example, the covariance matrix model can be improved with a
second factor, such as the performance of the transportation industry, that
would pick up the higher correlation between two stocks. With multiple
factors, the covariance matrix acquires a richer structure:
Cov = β1β′1σ 21 + . . . + βk β′kσ2k + Dε
The total number of parameters is (K + N × K + N), which may still be
considerably less than for the full model. With 100 assets and five factors,
for instance, the number is reduced from 5500 to 605, which is no minor
Factor models are also important because they can help us decide on
the number of VaR building blocks for each market. Consider, for instance,
a government bond market that displays a continuum of maturities ranging from one day to 30 years. The question is, how many VaR building
blocks do we need to represent this market adequately?
To illustrate, consider an equity market—say, the Swiss equity market—and calculate the principal components for the returns of the securities
of the Swiss Mark Index (SMI). The next step is to regress in an orthogonal
space the principal components against the factors, which can best explain
the principal components (variation of returns). The principal components
are by construction orthogonal. The factors contain multicolinearity, and,
through an additional condition during the Lagrange optimization—introduction of unit vectors with components summing to 1—a series of vectors
can be estimated that provide the best explanation of diagonal terms (the
common factors, e.g., the market) and are orthogonal to each other. The results are presented in Table 5-11. Principal component 1 can be best explained
by the Euro Currency Swiss Franc 1 Month factor, explaining 42.28 percent of
the principal component. With an R2 of 15.03, the second principle component was acceptably explained by the EFFAS Switzerland Government Bond
Index, but the result was already considerably weaker, as reflected in the corresponding statistics. The following factors do not fully help us understand
the return variation. However, the overall impact of such a multifactor model
is to help us understand more than we would using solely a diagonal model,
as it breaks down the common factor into several multiple factors.
Table 5-12 illustrates the relationship between the principal components and the factors. The factor loadings of the factors to the principal com-
T A B L E 5-11
Principal Component and Factor Combination
F Value
Euro Currency Swiss
Franc 1 Month
EFFAS Switzerland
Euro Currency German
Mark 7 Days
Standard & Poor’s
500 Composite
Euro Currency German
Mark 3 Months
EFFAS Germany
Benchmark Bond
over 5 Years
FTSE100 Index
EFFAS U.S. Government
over 5 Years
EFFAS Germany
Reto R. Gallati, “Empirical Application of APT Multifactor-Models to the Swiss Equity Market,” Basic Report, Zurich: Credit
Suisse Investment Research, September 1993.
T A B L E 5-12
Correlation of Principal Components to Factors from 08/08/1988 to 03/31/1993
Reto R. Gallati, “Empirical Application of APT Multifactor-Models to the Swiss Equity Market,” Basic Report, Zurich: Credit Suisse Investment Research, September 1993.
T A B L E 5-13
Risk Premiums for Multifactor Models after Burmeister/McElroy
Euro Currency
Swiss Franc 1 Month
EFFAS Switzerland
Euro Currency
German Mark 7 Days
Standard & Poor’s
500 Composite
Euro Currency German
Mark 3 Months
EFFAS Germany
Benchmark Bond
EFFAS Japan Government
over 5 Years
FTSE100 Index
EFFAS U.S. Government
over 5 Years
EFFAS Germany
t Distribution
Reto R. Gallati, “Empirical Application of APT Multifactor-Models to the Swiss Equity Market,” Basic Report, Zurich: Credit Suisse Investment Research, September 1993.
T A B L E 5-14
Correlations of SMI Securities on Excess Returns
Reto R. Gallati, “Empirical Application of APT Multifactor-Models to the Swiss Equity Market,” Basic Report, Zurich: Credit Suisse Investment Research, September 1993.
T A B L E 5-15
Factor Loadings According to Multifactor Calculations for SMI, Compiled 02/14/1992
R 2 Adjusted
SMI Security
Alusuisse-Lonza BS
Ciba-Geigy BS
Ciba-Geigy RS
CSHolding BS
Holderbank BS
Nestlé BS
Nestlé RS
Roche DRC
Schweizer Rück PC
Swissair BS
Winterthur BS
Zurich BS
Reto R. Gallati, “Empirical Application of APT Multifactor-Models to the Swiss Equity Market,” Basic Report, Zurich: Credit Suisse Investment Research, September 1993.
ponents are highlighted with bold numbers. In this context, the sign is not
relevant, but the absolute correlation is important. The factor sensitivity reflects the sign with a positive or a negative factor sensitivity (factor-beta βi).
Table 5-13 shows the risk premiums associated with this specific multifactor model. The available test lambdas confirm the selection of five indices according to the risk premium from the two-stage least-squares
procedure. On a basis of the results, the selected risk factors represent socalled priced factors, that is, factors that are rewarded with a risk premium
because they significantly influence the return on Swiss equities at the corresponding level. From the test statistics of the principal component analysis, the risk premium, and other analysis, we can conclude that the following
four factors are of sufficient significance for use in a multifactor APT model:
Euro Currency Swiss Franc 1 Month
EFFAS Switzerland Government
Euro Currency German Mark 3 Months
FTSE100 Index
Table 5-14 displays the correlations between the securities, highlighting the fact that for a small market like the Swiss equity market, the
correlations between the securities can be small, offering good diversification but requiring different approaches in the return and risk evaluation,
as the companies in the different sectors are exposed to different industry
factors and different company-specific factors.
Table 5-15 provides a summary of the results and contains the betas
of the securities to the defined factors as analyzed and evaluated in the
previous statistical procedures.
This decomposition shows that the risk of an equity portfolio can be
usefully summarized by its exposures to a limited number of factors. Different types of models exist, such as models that keep the factors constant
and allow tracking the same factors over time. Other models estimate the
factors on a regular basis and provide insight into the different factors as
they change over time and keep the overall explanatory power high.
Although VaR provides a line of defense against financial risks, it is no
panacea. Users must understand the limitations of VaR measures.
Event and Stability Risks
The main drawback of models based on historical data is that they assume
that the recent past is a good projection of future randomness. Even if the
data has been perfectly fitted, there is no guarantee that the future will not
hide nasty surprises that did not occur in the past.
Surprises can take two forms: either one-time events (such as a devaluation or default) or structural changes (such as going from fixed to
floating exchange rates). Situations where historical patterns change
abruptly cause havoc with models based on historical data.
Stability risk can be addressed by stress testing (discussed in Section
5.6.4), which aims at addressing the effect of drastic changes on portfolio
risk. To some extent, structural changes can also be captured by models
that allow risk to change through time or by volatility forecasts contained
in options. An example of structural change is the 1994 devaluation of the
Mexican peso, which is further detailed in the following text.
In December 1994, the emerging market turned sour as Mexico devalued the peso by 40 percent. The devaluation was widely viewed as having been bungled by the government, and led to a collapsing Mexican stock
market. Investors who had poured money into the developing economies
of Latin America and Asia faced large losses as the Mexican devaluation
led to a widespread decrease in emerging markets all over the world.
Figure 5-10 plots the peso-dollar exchange rate, which was fixed
around 3.45 pesos for most of 1994 and then jumped to 5.64 by midDecember. Figure 5-11 shows the distribution of the peso-dollar exchange
rates for the same time frame. Apparently, the devaluation was widely
unanticipated, even with a ballooning current account deficit running at
10 percent of Mexico’s GDP and a currency widely overvalued according
to purchasing power parity.
This episode indicates that, especially when price controls are left in
place for long periods, VaR models based on historical data cannot capture potential losses. These models must be augmented by an analysis of
economic fundamentals and stress testing. Interestingly, shortly after the
F I G U R E 5-10
Daily returns (ln)
Mexican peso / U.S. $
Mexican Peso–U.S. Dollar Exchange Rate from 1993 to 1996. (Data source:
Bloomberg Professional.)
Building Blocks for Integration of Risk Categories
F I G U R E 5-11
Distribution of Mexican Peso–U.S. Dollar Exchange Rates from 1993 to 1996, Including (left) and Excluding (right) the Week Before and After the Devaluation.
(Data source: Bloomberg Professional.)
Normal distribution
Current distribution
Normal distribution
Current distribution
devaluation, the Mexican government authorized the creation of currency
futures on the peso. It was argued that the existence of forward-looking
prices for the peso would have provided market participants, as well as
the central bank, with an indication of market pressures. In any event, this
disaster was not blamed on derivatives.
5.8.2 Transition Risk
Whenever there is a major change, a potential exists for errors. This applies, for instance, to organizational changes, expansion into new markets
or products, implementation of a new system, or new regulations. Since
existing controls deal with existing risks, they may be less effective during
a transition.
Transition risk is difficult to deal with because it cannot be explicitly
modeled. The only safeguard is increased vigilance in times of transition.
Changing Holdings
A similar problem of instability occurs when trying to extrapolate daily
risk to a longer horizon, which is of special concern to bank regulators.
As we have seen in Secs. 3.6.2 and, the typical adjustment is by a
square root of time factor, assuming constant positions. However, the
adjustment ignores the fact that the trading position might very well
change over time in response to changing market conditions. There is no
simple way to assess the impact on the portfolio VaR, but it is likely that
prudent risk management systems will decrease risk relative to conventional VaR measures. For instance, the enforcement of loss limits will
gradually decrease exposure as losses accumulate. This dynamic trading
pattern is similar to purchasing an option that has limited downside potential. It is also possible, however, as Barings has demonstrated, that
traders who lose money increase their bets in the hope of recouping their
Problem Positions
Problem positions are in a category similar to transition. All the analytical
methods underlying VaR assume that some data is available to measure
risks. However, for some securities, such as infrequently traded emerging market stocks, private placements, or exotic currencies, meaningful
market-clearing prices may not exist.
Without adequate price information, risk cannot be assessed from
historical data (not to mention implied data). Yet, a position in these assets
will create the potential for losses that is difficult to quantify. In the absence of good data, educated stress testing appears to be the only method
to assess risks.
5.8.5 Model Risks
Most risk management systems use past history as a guide to future risks.
However, extrapolating from past data can be hazardous. This is why it is
essential to beware of the pitfalls of model risks. Functional Form Risk
This is the purest form of model risk. Valuation errors can arise if the specific functional form selected for valuing a security is incorrect. The BlackScholes model, for instance, relies on a rather restrictive set of assumptions
(geometric Brownian motion, constant interest rates, and volatility). For
conventional stock options, departures from these assumptions generally
have few consequences. However, there are situations where the model is
inappropriate, such as for short-term interest rate options.
Model risk also becomes more dangerous as the instrument becomes
more complicated. Pricing CMOs requires heavy investments in the development of models, which may prove inaccurate under some market
conditions. Parametric Risk
Also known as estimation risk, parameter risk stems from imprecision in
the measurement of parameters. Even in a perfectly stable environment,
we do not observe the true expected returns and volatilities. Thus, some
random errors are bound to happen just because of sampling variation.
As shown in the previous chapters, the effect of estimating risk could
be formally assessed by replacing the sample estimates with values that
Building Blocks for Integration of Risk Categories
are statistically equivalent. An alternative method consists of sampling
over different intervals. If the risk measures appear to be sensitive to a
particular sample period, then estimation risk may be considerable.
Estimation risk increases with the number of estimated parameters.
The more parameters that are estimated, the greater the chance that errors
will interact with each other and create a misleading picture of risk. Errors
in correlations are particularly dangerous when they are associated with
large arbitrage positions. Parsimony breeds robustness.
The problem of estimation risk is often ignored in VaR analyses.
Users should realize the fundamental trade-off between using more data,
which leads to more precise estimates, and focusing on more recent data,
which may be safer if risk changes over time.
Unfortunately, data may not be available for very long periods. For
instance, only very limited histories are available for emerging markets or
exotic currencies. This is all the more reason to remember that VaR numbers are just estimates. Data Mining Risk
This is among the most insidious forms of risk. It occurs when searching
various models and reporting only the one that gives positive results. This
is particularly a problem with nonlinear models (such as neural network
or chaos models), which involve searching not only over parameter values
but also over different functional forms.
Data mining also consists of analyzing the data until some significant relationship is found. For instance, consider an investment manager
who tries to find calendar anomalies in stock returns. The manager tries
to see whether stock returns systematically differ across months, weeks,
days, and so on. So many different comparisons can be tried that, in 1
case out of 20, we would expect to find significant results at the usual 5
percent level. Of course, the results are significant only because of the
search process, which discards nonsignificant models. Data mining risk
manifests itself in overly optimistic simulation results based on historical
data. Often, results break down outside the sample period because they
are fallacious.
Data mining risks can be best addressed by running paper portfolios, where an objective observer records the decisions and checks how the
investment process performs using actual data. Survivorship Risk
Survivorship is an issue when an investment process only considers series, markets, stocks, bonds, or contracts that are still in existence. The
problem is that assets that have fared badly are not observed. Analyses
based on current data, therefore, tend to project an overly optimistic
image or display certain characteristics.
Survivorship effects are related to the “peso problem” in the foreign
exchange market. Before the devaluation of 1982, the Mexican peso was
selling at a large discount in the forward market (the forward price of the
peso was well below the price for current delivery). This discount rationally anticipated a possible devaluation of the peso. An observer analyzing
the discount before 1982 would have concluded that the market was inefficient. The failure, however, was not that of the market, but rather of the
observer, who chose a sample period in which the data did not reflect any
probability of a devaluation.
More generally, unusual events that have a low probability of occurrence but that may have severe effects on prices, such as wars or nationalizations, are not likely to be well represented in samples, and may be
totally omitted from survivorship series. Unfortunately, these unusual
events are very difficult to capture with conventional risk models.
5.8.6 Strategic Risks
As explained in Chapter 1, VaR can help to measure and control financial
risk. However, it is impotent in the face of strategic risks that pose a challenge to corporations. Strategic risks are those resulting from fundamental
shifts in the economy or political environment. One such example is the
story of Bankers Trust, which before 1994 was widely admired as a leader
in risk management, but became a victim of the backlash against derivatives. (See analysis of case studies in Section 6.1.) The derivatives market
has been subject to political and regulatory risks, which are part of the
menagerie of strategic risks affecting corporations either at the firm or the
industry level.
Political risks arise from actions taken by policy makers that significantly affect the way an organization runs its business. These policies may
impose limitations on the use of derivatives, thus negatively affecting the
profitability of many firms involved in that market. It is perhaps in response to these threats that the private sector has come up with initiatives
to address the issue of measuring market risks.
Regulatory risks are the result of changes in regulations or interpretation of existing regulations that can negatively affect a firm. For instance, as
a result of the Bankers Trust case, the Commodities and Futures Trading
Commission (CFTC) and the Securities and Exchange Commission (SEC)
have extended their jurisdiction over market participants by declaring
swaps to be “futures contracts” and “securities,” respectively. This has allowed the CFTC to classify Bankers Trust as a commodity trading advisor
subject to specific statutes. Another example is recent guidelines by federal
bank regulators prohibiting the sale of certain types of structured notes to
money market mutual funds, small savings institutions, and community
Building Blocks for Integration of Risk Categories
Time Aggregation
If return is seen as the first derivative (momentum) of an asset, risk can be
considered as a derivative of return and thus the second derivative (momentum) of the asset. It is important to understand what role time plays in
this calculation.
Computing VaR first requires defining the period of time during
which unfavorable outcomes can be measured. This period may be hours,
days, or weeks. The time horizon is different depending on the purpose of
the information. For an investment manager, it may correspond to the regular monthly or quarterly reporting period. For a trader, the horizon
should be sufficiently long to catch traders taking positions in excess of
their limits. Regulators are now leaning toward enforcing a horizon of two
weeks, which is viewed as the period necessary to force bank compliance.
To compare risk across horizons, we need a translation method, a
problem known in econometrics as time aggregation. Suppose we observe
daily data, from which we obtain a VaR measure. Using higher-frequency
data is generally more efficient because it uses more information. The investment horizon, however, may still be three months. The distribution
for daily data must now be transformed into a distribution over a quarterly horizon. If returns are uncorrelated over time (or behave like a random walk), this transformation is straightforward.
冢 冣
Rt,2 = ln ᎏ
Pt − 2
冢 冣
冢 冣
Pt − 1
= ln ᎏ + ln ᎏ
Pt − 1
Pt − 2
= Rt − 1 + Rt
The problem of time aggregation can be traced to the problem of
finding the expected return and variance of a sum of random variables.
From Equation (5.48), the two-period return (from t − 2 to t) Rt,2 is equal to
Rt − 1 + Rt, where the subscript 2 indicates that the time interval is two periods. Following a Brownian motion, we know that:
E(X1 + X2) = E(X2)
σx1 + x2 = σx1 + σx2 + 2σx1, x2
Expressed formally, a variable z (X1 − Xn) follows a Wiener process if
it has the following two properties. First, the change ∆z during a small period of time ∆t is:
∆z = ε兹∆t
where ε is a random drawing from a standardized normal distribution
N(0,1). Second, the values of ∆z for any two different short intervals of
time ∆t are independent.
It follows from the first property that ∆z itself has a normal distribution with:
Mean of ∆z = 0
Standard deviation of ∆z = 兹∆t
Variance of ∆z = ∆t
The second property implies that z follows a Markow process. Consider the increase in the value of z (distance between two observations)
during a relatively long period of time T. This can be denoted by z(T) − z(0)
and can be regarded as the sum of the increases in z in N small time intervals of length ∆t, where:
It follows that:
z(T) − z(0) = 冱 εi 兹∆t
where εi (i = 1,2, . . . ,N) are random drawing from N(0,1). From the second
property of the Wiener processes, the εi values are independent of each
other. It follows from Equation (5.54) that z(T) − z(0) is normally distributed with:
Mean of [z(T) − z(0)] = 0
Standard deviation of [z(T) − z(0)] = N∆t = T
Variance of [z(T) − z(0)] = 兹T
This is consistent with the discussion earlier in this section in regard
to time aggregation of the expected return and variance of a sum of random variables.
The key assumption has to be verified to allow a straightforward application of time aggregation: to aggregate over time, we assume that returns are uncorrelated over any successive time intervals, following a
Brownian motion. This assumption is consistent with efficient markets,
Building Blocks for Integration of Risk Categories
where the current price includes all relevant information about a particular asset at any time. If so, all price changes must be due to news that, by
definition, cannot be anticipated and therefore must be uncorrelated over
time: prices follow a random walk. The cross-product term σx1,x2 must then
be 0. In addition, we could reasonably assume that returns are identically
distributed over time, which means that E(Rt − 1) = E(Rt) = E(R) and that
σ(Rt − 1) = σ(Rt) = σ(R).
Based on these two assumptions, the expected return over a twoperiod horizon is E(Rt,2) = E(Rt − 1) + E(Rt) = 2E(R). The variance is σ(R1,2) =
σ(Rt − 1) + σ(Rt) = 2σ(R). The expected return over two days is twice the expected return over one day; likewise for the variance. Both the expected
return and the variance increase linearly with time. However, volatility, in
contrast, grows with the square root of time. In summary, to go from daily,
monthly, or quarterly data to annual data, we can write:
µ = µannualT
σ = σannual 兹T
where T is the number of periods over the time horizon, usually in fractions relative to one year (e.g., 1⁄12 for monthly data or 1⁄252 for daily data if
the number of trading days in a year is 252). Therefore, adjustments of
volatility for different horizons can be based on a square root of time factor when positions are constant over time.
As an example, let us go back to the German mark–U.S. dollar rate
data that we wish to convert to annual parameters. The mean of changes is
−0.21% per month × 12 = −2.6% per annum. The risk is 3.51% per month ×
√12 = 12.2% per annum.
Table 5-16 compares the risk and average return for a number of financial series measured in percent per annum over the period from 1973
to 1994. Stocks are typically the most volatile of the lot (15 percent). Next
come exchange rates against the dollar (12 percent) and U.S. bonds (9 per-
T A B L E 5-16
Risk and Return, 1973 to 1994 (Percent per Annum)
German Mark
cent). Some currencies, however, are relatively more stable. Such is the
case for the French franc versus the German mark, which have been fixed
to each other since March 1979.
Keep in mind that since the volatility grows with the square root of
time and the mean with time, the mean will dominate the volatility over
long horizons. Over short horizons, such as a day, volatility dominates.
This provides a rationale for focusing on measures of VaR based on
volatility only and ignoring expected returns. It also provides a rationale
for analyzing the appropriateness of time horizon assumptions between
different risk models. Whereas market risk information is readily available in different frequencies and formats, credit risk information is difficult to receive on a broad basis. This means that any data quality issue or
low data frequency will lead to return information that contains errors. Errors will be maximized by any transformation through multiplication
with the square root of time to adjust volatility from short to long time
To illustrate this point, consider an investment in U.S. stocks that, according to Table 5-16, returns an average of 11.1 percent per annum with a
risk of 15.4 percent. Table 5-17 compares the risks and average returns of
holding a position over successively shorter intervals, using Equations
(5.56) and (5.57). Going from annual to daily and even hourly data, the
mean shrinks much faster than the volatility. Based on a 252-trading-day
year, the daily expected return is 0.04 percent—very small compared to
the volatility of 0.97 percent.
Table 5-17 can be used to infer the probability of a loss over a given
measurement interval. For annual data, this is the probability that the re-
T A B L E 5-17
Risk and Return over Various Horizons Based on Average Volatility
for S&P 500 Index from July 1989 to July 2001
of Loss (%)
Bloomberg Professional.
Building Blocks for Integration of Risk Categories
turn, distributed N(µ = 11.1%, σ2 = 15.4%2), falls below 0. Transforming to a
standard normal variable, this is the probability that ε = (R − 0.111)/0.154
falls below 0, which is the area to the left of the standard normal variable
−0.111/0.154 = −0.7208. From normal tables, we find that the area to the left
of 0.7208 is 23.6 percent. Thus, the probability of losing money over a year is
23.6 percent, as shown in the last column of Table 5-17. In contrast, the probability of losing money over one day is 48.2 percent, which is much higher!
This observation is sometimes interpreted as support for the conventional wisdom that stocks are less risky in the long run than over a
short horizon. Unfortunately, this is not necessarily correct, since the dollar amount of the loss also increases with time.20 The statistical tools necessary to compute VaR are discussed in the next section.
Predicting Volatility and Correlations
The volatility of financial markets and instruments can be observed and is
to a certain extent predictable, which has substantial impact on risk management. Increasing volatility will lead to higher VaR. However, the observation and estimation of volatility do not follow a linear projection from
the past into the future. Reviewing some historical time series regarding
the stability of risk, it becomes obvious that the risk profile changes over
time. For exchange rates this is intuitively obvious, as regime changes impact the risk profile. For example, return patterns changed dramatically
after President Richard Nixon ended the 1944 Bretton-Woods agreement
on August 15, 1971, declaring that the U.S. government no longer supported the gold-dollar exchange rate at $35 per fine ounce. On March 16,
1973, the exchange rates of the industrialized countries became freefloating. Bond yields were also more volatile and had a different risk profile in the early 1980s, as the creation of Brady bonds was a driving factor
to eliminate systemic and counterparty risk. These examples demonstrate
structural changes to risk. As a consequence, investors have to review their
portfolios to reduce their exposures to those assets whose volatility is predicted to increase. Also, forecasted volatility means that assets directly dependent on volatility, such as derivatives, will change in value in a
predictable fashion. Additionally, in a rational market, equilibrium prices
will be affected by changes in volatility. A better understanding of the risk
profiles, and thus the volatilities, enables participants in the market to better predict changes in volatility, diversification, exposures, and hedges, and
thus to better control financial market risks.
Figure 5-12 shows return and volatility data over several years and
different time series. Several periods are of particular interest: the Asian
crisis, starting in July 1997; the Russian crisis in September/October 1998;
and the technology, media, and telecommunications (TMT) sectors crisis
in April 2000. 1998 was particularly tumultuous—the Russian crisis was
F I G U R E 5-12
S&P 500 Index Returns from July 1989 to July 2001. (Data source: Bloomberg
Russian crisis TMT bubble
S&P 500 index daily return
linked to LTCM hedge fund speculation on the narrowing of bond spreads
in Russia, which increased volatility dramatically. April 2000 was another
interesting period, as the TMT sectors abruptly downturned after almost
10 years of uninterrupted growth. The following sections discuss techniques of estimating and forecasting variation in risk and correlations.
5.8.9 Modeling Time-Varying Risk Risk Around Mean and Fat Tail Events
To illustrate our point, we will use the S&P 500, the FTSE, and the Nasdaq
to analyze the risk profiles and changes over time. In Figure 5-12 the S&P
500 index returns are displayed from July 1989 to July 2001. The period
from 1990 to 1996 was fairly typical, with mostly narrow trading ranges
and some wide swings. The years 1994 to 1996 were characterized by a
steady upside in the equity markets with narrow volatilities, following the
unexpected increase in lending rates by the Federal Reserve in February
1994. The result was increased volatilities and a bad year for the fixed income market with steady inflows to the equity market. The average
volatility from 1994 to 1996 was 9.5 percent (using a 252-trading day ad-
Building Blocks for Integration of Risk Categories
justment). Volatility was not constant over time. More important is that
the time variation in risk could explain the fact that the empirical distribution of return does not fit a normal distribution. The empirical distribution is better explained by a leptokurtotic distribution than a normal
distribution, as we will see later.
The fat tails are of particular interest because the deviation of the empirical profile from the normal distribution profile causes issues with risk
modeling, hedging, etc. (see Figure 5-13). Two obvious alternative hypotheses can explain fat tails:
1. The first explanation is that the true distribution is stationary
and the empirical return distribution contains fat tails. In this
case a normal distribution approximation is inappropriate.
2. The alternative view is that the distribution does change over
time. Consequently, in times of increased volatilities in the markets, a stationary model could measure large observations as
outliers, whereas they are really drawn from a distribution with
temporarily greater dispersion.
In reality, both explanations carry some truth. This is why forecasting volatility is particularly critical for risk management. In the following
section, we will focus on traditional approaches based on parametric time
series modeling.21 Moving Averages
A very simple but widely employed method is to use a moving window of
fixed length to estimate volatility. For instance, a typical length is 20 trading days (about a calendar month) or 60 trading days (about a calendar
F I G U R E 5-13
Distribution of the Nasdaq Index Returns for 2000, 1999, and 1998 (left to right). (Data
source: Bloomberg Professional.)
Normal distribution
Current distribution
Normal distribution
Current distribution
Normal distribution
Current distribution
Assuming that we observe returns r over n days, this volatility estimate is constructed from a moving average (MA):
− r苶)
冱 (r莦
In Equation (5.58), we focus on absolute returns instead of returns
around the mean. The second approach (Equation 5.59) includes the expected returns for the volatility estimation. We will use the second approach for the following calculations.
Each day, the volatility forecast is updated by adding information
from the preceding day and dropping information from (n + 1) days ago. All
weights on past returns are equal and set to (1/n). While simple to implement, this model has serious drawbacks. Most important, it ignores the dynamic ordering of observations. Recent information receives the same
weight (importance) as older information, but recent data should intuitively
be more relevant. For example, if there was a large return n days ago, dropping this return as the window moves one day forward will substantially affect the volatility estimate. As a result, moving average measures of
volatility tend to look like levels of width n when plotted against time.
Figure 5-14 displays 20-day and 60-day moving averages for the S&P
500 index changes. Movements in the 60-day average are much more stable
than those in the 20-day average. This is understandable, because longer periods decrease the weight of any single day. But is the longer time horizon
adding value? Longer periods increase the precision of the estimate but could
miss underlying variation in volatility. The answer to this question is left open
to the investor, depending on his or her time horizon and other parameters. GARCH Estimation
As mentioned earlier, longer periods increase the precision of the estimate
but could miss underlying variation in volatility. This is why volatility
estimation has moved toward models that put more weight on recent
information. One of the first approaches to modeling volatility with a
time-dependent component was the generalized autoregressive heteroskedastic (GARCH) model proposed by Engle and Bollerslev.22
The GARCH approach assumes that the variance of returns follows a
predictable process. The forecasted conditional variance depends on the latest observation but also on the previous conditional variance. Define h as
the conditional variance, using information up to time t − 1, and rt − 1 as the
previous day’s return. The simplest such model is the GARCH (1,1) process:
ht = α0 + α1r2t − 1 + βht − 1
Building Blocks for Integration of Risk Categories
F I G U R E 5-14
Moving Average (MA) Volatility Forecasts for Mexican Peso–U.S. Dollar Foreign
Exchange. (Data source: Bloomberg Professional.)
Volatility MA(20)
Volatility MA(60)
The average unconditional variance is found by setting
E[r2t − 1] = ht = ht − 1 = h
Solving for h, we find:
h = ᎏᎏ
1 − α1 − β
For this model to be stationary, the sum of parameters α1 + β must be
less than unity. This sum is also called the persistence, for reasons that will
become clear later on. This specification provides a parsimonious model,
with few parameters, that seems to fit the data quite well.23
GARCH models have become a mainstay of time series analyses of
financial markets, which systematically display volatility clustering. Literally hundreds of papers have applied GARCH models to stock return
data,24 to interest rate data,25 and to foreign exchange data.26 Econometricians have also created many variants of the GARCH model, most of
which provide marginal improvement on the original GARCH model. A
comprehensive review of the GARCH literature has been generated by
Bollerslev, Chou, and Kroner.27 The drawback of GARCH models is their
nonlinearity. The parameters mentioned earlier must be estimated regularly by maximization of the likelihood function, which involves a numerical optimization. Typically, researchers assume that the scaled residual
εt = ᎏ
has a normal distribution.
The GARCH approach provides other interesting features. The returns r can be serially uncorrelated but are not independent as they are
nonlinearly related through second moments. This class of models is also
related to chaos theory. Recent work has revealed that many financial
prices display chaotic properties. Often, the nonlinearities behind chaos
theory can be traced to the time variation in variances. The GARCH models can explain some of the reported chaotic behavior of financial markets.
Figure 5-15 shows the GARCH forecast of volatility for the S&P 500
index changes. It shows increased volatility from fall 1996 on. Afterward,
volatility spikes upward during the Asian crisis in summer 1997, the RusF I G U R E 5-15
GARCH Volatility Forecast for the S&P 500 Index. (Data source: Bloomberg
1 SD GARCH volatility forcast
Building Blocks for Integration of Risk Categories
sian crisis in September/October 1998, and the TMT meltdown in April
2000 and the months following. A simple Autoregressive Integrated Moving Average (ARIMA) test run on the S&P index (Figure 5-16) shows that
the assumption of stable volatility is closer to an acceptable level (p value
≥ 0.05) in the years until 1996. After 1996, the p values show clearly unacceptable low levels.
The practical application of this information is illustrated in Figure
5-17, which shows daily returns along with conditional 95 percent confidence bands. This model appears to adequately capture variation in risk.
Most of the returns fall within the 95 percent band. The few outside the
bands correspond to the remaining 5 percent of occurrences. Long-Horizon Forecasts
The GARCH approach can also be used to compute volatility over various
time horizons. We assume that the volatility is estimated based on daily
information. To compute a monthly volatility, we first decompose the
multiperiod (geometric) return into daily returns as in Equation (5.63):
F I G U R E 5-16
ARIMA Test for S&P 500 Index. (Data source: Bloomberg Professional.)
Plot of standardized residuals
ACF plot of residuals
PACF plot of residuals
P values of Ljung-box chi-squared statistics
p value
F I G U R E 5-17
Returns and GARCH Confidence Bands for S&P 500 Index. (Data source:
Bloomberg Professional.)
S&P 500 Index
冢 冣
2 SD band
冢 冣
–2 SD band
Pt − 1
Rt,2 = ln ᎏ = ln ᎏ + ln ᎏ = Rt − 1 + Rt
Pt − 2
Pt − 1
Pt − 2
冢 冣
rt,T = rt + rt + 1 + rt + 2 + . . . + rT
If returns are uncorrelated across days, the long-horizon variance as
of t − 1 is:
Et − 1 [rt,T] = Et − 1 [r 2t ] + Et − 1 [r 2t + 1] + Et − 1 [r 2t + 2] + . . . + Et − 1 [r 2T]
After some transformation, the forecast of variance τ days ahead is:
1 − (α1 + β)τ
Et − 1 [r2t + τ] = α0 ᎏᎏ + (α1 + β)τ ht
1 − (α1 + β)
Figure 5-18 displays the effect of different persistence parameters
α1 + β on the variance. We start from the long-run value for a given variance, 0.5. Then a shock moves the conditional variance to twice its value,
Building Blocks for Integration of Risk Categories
F I G U R E 5-18
Persistence Parameters on the Variance.
Persistence parameters
Average variances
Initial shock
Forecasting n days ahead
1.0. High persistence means that the shock will decay slowly. For instance,
with a persistence of 0.986, the conditional variance is still 0.90 after 20
days. With a persistence of 0.8, the variance drops very close to its longrun value only after 20 days. The dots on each line represent the average
daily variance over the following 25 days. High persistence implies that
the average variance will remain high.
The parabolic shape of the behaving persistence parameters looks
very similar to the cone of forecasted volatilities using the VaR estimates
as calculated with the RiskMetrics approach (see Figure 5-19).
5.8.10 The RiskMetrics Approach
RiskMetrics takes a pragmatic approach to modeling risk.28 Variance forecasts are modeled using an exponential weighting schema. Formally, the
forecast for time t is a weighted average of the previous forecast, using
weight λ (Equation 5.67), and of the latest squared innovation, using
weight (1 − λ) (Equation 5.68):
F I G U R E 5-19
S&P 500 Returns and VaR Estimates (1.65σ) (Source: J. P. Morgan, RiskMetrics
Technical Document,” 4th ed., New York: J. P. Morgan, December 1996, chart 5.4.
Copyright © 1966 by Morgan Guaranty Trust Company, all rights reserved. Reproduction with permission of RiskMetrics Group, LLC.)
− r苶)
冱 (r 莦
冪莦ᎏT1 莦
(1 − λ) 冱 λt − 1 (rt − r苶)2
In comparing the two estimators (equal and exponential), the exponentially weighted moving average model depends on the parameter
0 < λ < 1.
The λ parameter is called the decay factor, and must be less than unity.
It determines the relative weights that are applied to the observations (returns) and the effective amount of data used in estimating volatility. This
model can be viewed as a special case of the GARCH process, where α0 is
set to 0 and α1 and β sum to unity. The model therefore allows for persistence. As shown in Figure 5-20, it appears to produce results that are very
close to those achieved with the GARCH model.
Building Blocks for Integration of Risk Categories
F I G U R E 5-20
Mean Reversion for the Variance (Source: J. P. Morgan, RiskMetrics Technical
Document,” 4th ed., New York: J. P. Morgan, December 1996, chart 5.9. Copyright © 1996 by Morgan Guaranty Trust Company, all rights reserved. Reproduction with permission of RiskMetrics Group, LLC.)
a exp(t)
A particularly interesting feature of the exponentially weighted estimator is that it can be written in a recursive form, which, in turn, will be
used as a basis for making volatility forecasts. In order to derive the recursive form, it is assumed that an infinite amount of data is available. For
example, assuming that the sample mean is zero, we can derive the period
t + 1 variance forecast, given data available at time t (one day earlier) as:
σ 21,t + 1|t = λσ21,t − 1|t + (1 − λ) r 21, t
The one-day RiskMetrics volatility forecast is given by:
σ1,t + 1|t = 兹λσ
λ) r21,t苶
1,t − 1苶−
|t + (1 苶
The subscript t + 1|t is read “the time t + 1 forecast given information
up to and including time t.” The subscript t − 1 1|t is read in a similar fashion. This notation underscores the fact that RiskMetrics is treating the
variance (volatility) as time dependent. The fact that this period’s variance
forecast depends on last period’s variance is consistent with the observed
autocorrelation in squared returns. The volatility is given by:
σ21,t + 1|t = (1 − λ) 冱 λir21,t − 1
= (1 − λ)(r 21,t + λr 21,t − 1 + λ2r 21,t − 2 + . . .)
= (1 − λ)r 21,t + λ(1 − λ)(r 21,t − 1 + λr 21,t − 1 + λ2r21,t − 2 + λ2r21,t − 3)
= λσ21,t − 1|t + (1 − λ)r 21,t
The exponential approach is particularly easy to implement because
it relies on one parameter only and thus is more robust than other models
to estimation error. In addition, as was the case for the GARCH model, the
estimator is recursive; the forecast is based on the previous forecast and
the latest innovation. The whole history is summarized by one number,
ht − 1. This is in contrast to the moving average, for example, where the last
n returns must be used to construct the forecast.
The only parameter in this model is the decay factor λ. In theory, this
could be found by maximizing the likelihood function, but in practice, this
would be a daunting task to perform every day for all the time series in the
RiskMetrics database. In the original technical document, the analysis has
been performed on a basic set of core data based on 450 time series. An optimization has other shortcomings. The decay factor may vary across series and over time, thus decreasing consistency over different periods. In
addition, different values of λ create incompatibilities for the covariance
terms and may lead to coefficients of correlation greater than unity, as we
will see later. In the original document, RiskMetrics uses only one decay
factor for all series, which is set at 0.94 for daily data. However, RiskMetrics currently computes stress testing and VaR based on approximately
500,000 time series from the DataMetrics platform and allows users to define any combination of decay factors, lookback periods, and time horizons, which reflects the underlying data better than the original simplified
framework. This document also outlines how risk is computed at different
levels of aggregation (from subposition through the entire portfolio) and
discusses the various methodologies used (Monte Carlo simulations, historical simulations, etc.).29
RiskMetrics also provides risk forecasts over monthly horizons, defined as 25 trading days. In theory, the exponential model should be used
to extrapolate volatility over the next day, then the next, and so on until
the 25th day, as was done previously for the GARCH model (see Figure
5-21). The persistence parameter for the exponential model is unity. Therefore, it is based on the assumption that there is no mean reversion and the
monthly volatility should be the same as the daily volatility. In practice,
the estimator is identical to the exponentially weighted estimator at the
Building Blocks for Integration of Risk Categories
F I G U R E 5-21
Exponential Volatility Forecast for FTSE Index. (Data source: Bloomberg
Exponential weighted
beginning of this section, except that it defines innovations as the 25-day
variance. After experimenting with the data, J. P. Morgan chose λ = 0.97 as
the optimal decay factor. Therefore, the daily and monthly specifications
are inconsistent with each other. However, they are both easy to use, they
approximate the behavior of actual data quite well, and they are robust to
5.8.11 Modeling Correlations
Correlation is of unquestionable importance for portfolio risk—even more
so than individual variances. To illustrate the estimation of correlation, we
pick two series: the S&P 500 index and the FTSE 100 index.
Over the period from 1996 to 1998, the average daily correlation coefficient [MA(60)] was 0.333. However, we should expect some variation
in the correlation coefficient because this time period covers the Asian crisis and the Russian/LTCM crisis. The average correlation was 0.162 in
1995, 0.249 in 1996, 0.305 in 1997, and 0.331 in 1998. As in the case of variance estimation, various methods can be used to capture time variation in
correlation: moving average, GARCH, and exponential.
426 Moving Averages
The first method is based on moving averages (MAs), using a fixed window of length n. Figure 5-22 presents estimates based on an MA(20) and
MA(60). Correlations for the MA(20) start around 0.4 and move between
0.65 and −0.1 until March 1998, when correlation hits a low of −0.45, moving back to 0.7. The correlation falls from 0.76 at the end of January 1999 to
−0.34 by April 21, 1999. As can be seen in the figure, the MA(60) follows
with some lag and averaging of the swings. These estimates are subject to
the same criticisms as before. Moving averages place the same weight on
all observations within the moving window and ignore the fact that more
recent observations may contain more relevant information than older
ones. In addition, dropping observations from the window sometimes has
severe effects on the measured correlation. Exponential Averages
In theory, GARCH estimation could be extended to a multivariate framework. The problem is that the number of parameters to estimate increases
exponentially with the number of series. With two series, for instance, we
need to estimate nine terms, or three α1, α0, and β parameters for each of
F I G U R E 5-22
Moving Average–Based Correlation Between the S&P 500 Index and the FTSE
100 Index. (Data source: Bloomberg Professional.)
Correlation SPX/UKX
Building Blocks for Integration of Risk Categories
the three covariance terms. For larger samples of securities, this number
quickly becomes unmanageable.
The RiskMetrics approach is convincing in its simplicity. Covariances are estimated, much like variances, using an exponential weighting
h12,t = λh12,t − 1 + (1 − λ)r1,t − 1r2,t − 1
As before, the decay factor λ is arbitrarily set at 0.94 for daily data
and 0.97 for monthly data. The conditional correlation is then:
ρ12,t = ᎏ
Figure 5-23 displays the time variation in the correlation between the
S&P 500 index and the FTSE 100 index. The pattern of movements in correlations does not seem too different from the MA model, plotting somewhere between the MA(20) and MA(60).
F I G U R E 5-23
Exponential-Weighted Correlation Between the S&P 500 Index and the FTSE 100
Index. (Data source: Bloomberg Professional.)
Exponential weighted
Correlation SPX/UKX
Note that the reason why J. P. Morgan decided to set a common factor λ across all series is to ensure that all estimates of ρ are between −1 and
1. Otherwise, there is no guarantee that this will always be the case. Crashes and Correlations
It is intuitively obvious that low correlations help reduce portfolio risk. It
is often argued that correlations increase in periods of global turbulence.
Such an observation is particularly worrisome, because increasing correlations occurring at a time of increasing volatility would defeat the diversification properties of portfolios. Measures of VaR based on historical
data tend to seriously underestimate the actual risk of failure because both
risk and correlation are understated. This double blow could well lead to
returns that are far outside the range of forecasts.
Indeed, we expect the structure of the correlation matrix to depend on
the type of shocks affecting the economy. Global factors, such as the oil crises
and the Gulf War, create increased turbulence and increased correlations. For
instance, Longin and Solnik30 examined the behavior of correlations among
national stock markets and found that correlations typically increase by 27
percent (from 0.43 to 0.55) in periods of high turbulence. Assuming a large
苶), this implies that VaR should be
portfolio (where risk is proportional to 兹ρ
multiplied by a factor of √(0.55/0.43) = 1.13. Thus, based solely on the correlation effect, VaR measures could underestimate true risk by 13 percent.
The extent of bias, however, depends on the sign of positions. Higher
correlations are harmful to portfolios with only long positions, as is typical of equity portfolios. In contrast, decreasing correlations are dangerous
for portfolios with short sales.
Perhaps these discomforting results explain why regulators impose
large multiplicative factors on internally computed VaR measures. But
these observations also point to the need for stress simulations to assess
the robustness of VaR measures to changes in correlations.
Using Option Data
Measures of value at risk are only as good as the quality of forecasts of risk
and correlations. Historical data, however, may not provide the best available forecasts of future risks. Situations involving changes in regimes, for
instance, are simply not reflected in recent historical data. This is why it is
useful to turn to implied forecasts contained in the latest market data. Implied Volatilities
An important function of derivatives markets is arbitrage discovery. Derivatives provide information about market clearing prices, which includes the discovery of volatility. Options are assets whose prices are
influenced by a number of factors, all of which are observable save for the
volatility of the underlying price. By setting the market price of an option
Building Blocks for Integration of Risk Categories
equal to its model value, one can recover an implied volatility.31 Similarly,
implied correlations also can be derived from triplets of options, using, for
instance, the Margrabe pricing model.32
Correlations are also implicit in so-called quanto options, which also
involve two random input variables. For instance, a quantity-adjusted option would be an option struck on a foreign stock index where the foreign
currency payoff is translated into dollars at a fixed rate. The valuation formula for such an option also involves the correlation between two sources
of risk. Thus, options can potentially reveal a wealth of information about
future risks and correlations.
If options markets are efficient, the implied volatility should provide
the market’s best estimate of future volatility. However, options trading
means taking volatility bets. Expressing a view on volatility has become so
pervasive in the options markets that prices are often quoted in terms of
bid-ask volatility. As options reflect the market consensus about future
volatility, there are sound reasons to believe that options-based forecasts
should be superior to historical estimates.
The empirical evidence indeed points to the superiority of options
data. An intuitive way to demonstrate the usefulness of options data is to
analyze the Russian crisis in September to October 1998. Figure 5-24 comF I G U R E 5-24
Implied Volatility Forecasts for S&P Index Returns. (Data source: Bloomberg
Implied volatility
pares volatility forecasts during 1992, including those implied from S&P
500 index options and a moving average with a window of 60 days. It is intuitively obvious that the implied volatility immediately picks up the behavior of the market and reflects the expected volatility to justify current
market conditions. As options traders rationally anticipated greater turbulence, the implied volatility was much more useful than time series models. Conclusions
The empirical evidence shows that options contain a wealth of information
about price risk that is generally superior to time-series models. This finding is particularly useful in times of stress, when the market has access to
current information that is simply not reflected in historical approaches.
The drawback of option-implied parameters is that the volume and range
of traded options is not sufficiently wide to cover the volatility of all essential financial prices. As more and more options contracts and exchanges are
springing up all over the world, traded options data is more readily available. Historical data provides a backward-looking alternative.
The options-based credit model detailed in Section highlights the advantages of an options-based approach:
Using implied volatilities, the options-based model is forward
looking and can be applied in a similar context as the market
risk–based options model regarding time horizon.
The options model does not necessarily require a mean variance
normal distribution. Nonlinearity of the underlying asset is
captured with an options-based approach for market and credit
risk. Operational risk issues can be approached and covered in a
similar manner, based on the evaluation of the implied volatility
required to calculate the operational risk premium for the
historical operational losses as captured through a historical
operational risk database.
The approaches for market risk management under normal conditions traditionally have focused on the distribution of portfolio value changes resulting from moves in the midprice. Under this assumption, market risk is
really in a “pure” form: risk in an idealized market with no “friction” in obtaining a fair price. However, many markets possess an additional liquidity component that arises from a trader not realizing the midprice when
liquidating a position, but rather the midprice minus the bid-ask spread.
We argue that liquidity risk associated with the uncertainty of the
spread, particularly for thinly traded or emerging market securities under
adverse market conditions, is an important part of overall risk and therefore
Building Blocks for Integration of Risk Categories
an important component and a critical assumption of modeling. The current
regulative conceptual approach to measuring market risk does not consider
liquidity risk explicitly. Approaches have been developed for modeling liquidity risk that can be easily and seamlessly integrated into standard VaR
models.33 The BIS is inadvertently monitoring liquidity risk, but by not
modeling it explicitly and therefore capitalizing against it. Therefore, banks
will be experiencing surprisingly many violations of capital requirements,
particularly if their portfolios are concentrated in emerging markets. The
crash in October 1998 has shown the impact of inadequate liquidity in Russian bonds and the supposed adequacy of quantitative models.
Portfolios are usually marked to market at the middle of the bid-offer
spread, and many hedge funds used models that incorporated this assumption. In late August, there was only one realistic value for the portfolio: the
bid price. Amid such massive sell-offs, only the first seller obtains a reasonable price for its security; the rest lose a fortune by having to pay a liquidity
premium if they want a sale. . . . Models should be revised to include bidoffer behavior.34
The turmoil in the capital markets in October 1998 led experts and
laymen alike to cast liquidity risk in the role of the culprit. Inexperienced
and sophisticated players alike were caught by surprise when markets
dried up. Unsurprisingly, the first to go were the emerging markets in
Asia, and, more recently, in Russia. Then the crisis spilled over into the
U.S. corporate debt market, which was indeed much more surprising. One
of the most famous victims of the 1998 liquidity crisis was Long Term Capital Management (LTCM). Spreads appeared to widen out of the blue; but
this could have been predicted. More generally, it is a well-acknowledged
fact that the standard VaR concept used for measuring both market and
credit risk for tradable securities lacks a rigorous treatment of liquidity
risk. At best, the risk for large illiquid positions is adjusted upward in an
ad hoc fashion by utilizing a longer time horizon in the calculation of VaR
that at best is a subjective estimate of the likely liquidation time of the position. But this holding period adjustment is usually carried out using the
square root of time scaling of the variances and covariances rather than a
recalculation of variances and covariances for the longer time horizon.35
The combination of the recent rapid expansion of emerging market
trading activities and the recurring turbulence in those markets has
pushed liquidity risk to the forefront of market risk management research.
New work in asset pricing has demonstrated how liquidity as a driving
factor in risk measurement plays a key role in security valuation and optimal portfolio choice by effectively imposing endogenous borrowing and
short-selling constraints, as argued by Longstaff.36
Liquidity also plays a major role in transaction costs, as trades of large
illiquid positions typically execute at a price away from the midprice.
BARRA’s Market Impact Model and other such models quantify the market
impact cost, defined as the cost of immediate execution, for establishing and
liquidating large positions. Jarrow and Subramanian consider the effect of
trade size and execution lag on the liquidation value of the portfolio,37 proposing a liquidity-adjusted VaR measure that incorporates a liquidity discount, volatility of the liquidity discount, and volatility of the time horizon
to liquidation. Although this concept is attractive, there is no available data
or procedure to measure the model parameters such as mean and variances
for quantity discounts or execution lags for trading large blocks.
Illiquidity can arise from different sources. Conceptually we have to
distinguish between risk caused by uncertainty in asset returns and risk
due to liquidity constraints. The breakdown of liquidity risk allows a distinction between exogenous liquidity risk, which is not under control of
the market participant (market maker or trader), and endogenous liquidity risk, which is the under control of the trader and usually the result of
sudden unloading of large positions that the market is unable to absorb efficiently. Conceptually, the current models (which do not distinguish between uncertainty from asset returns or due to liquidity) ignore valuable
information contained in the distribution of bid-ask spreads.
Traditional market risk management (under normal conditions) usually deals exclusively with the distribution of portfolio value changes via
the distribution of asset/trading returns. These asset/trading returns are
based on the midprice, and thus the market risk is really in a “pure”
form—risk in an idealized market with no friction in obtaining the fair
price. However, many markets possess an additional liquidity component
that arises from traders not realizing the midprice when liquidating a position quickly or when the market is moving against them; instead, they
realize the midprice minus some spread. Marking to market therefore
yields an underestimation of the true risk in such markets, because the realized value on liquidation can deviate significantly from the market midprice. We argue that the deviation of this liquidation price from the
midprice, also referred to as the market impact or liquidation cost, and the
volatility of this cost, are important components to model in order to capture the true level of overall risk. We conceptually split uncertainty in
market value of an asset, i.e., its overall market risk, into two parts:
(1) uncertainty that arises from asset returns, which can be thought of as a
pure market risk component, and (2) uncertainty due to liquidity risk.
Conventional VaR approaches, such as J. P. Morgan’s RiskMetrics,
focus on capturing risk due to uncertainty in asset returns but ignore uncertainty due to liquidity risk. The liquidity risk component is concerned with
the uncertainty of liquidation costs. Conceptually, we can express these
ideas as a market/liquidity risk plane that considers the joint impact of the
two types of risk. Most markets and trading situations fall into regions 1 and
3; we observe that market risk and liquidity risk components are correlated
Building Blocks for Integration of Risk Categories
in most cases. For instance, FX derivative products in emerging markets
have high market and liquidity risks and therefore fall into region 1. The
spot markets for most G-7 currencies, on the other hand, will fall into region
3 due to the relatively low market and liquidity risks involved. Most normal
trading activity occurs in these two regions and is subject to exogenous liquidity risk, which refers to liquidity fluctuations driven by factors beyond
individual traders’ control. We distinguish this from endogenous liquidity
risk, which refers to liquidity fluctuations driven by individual actions, such
as an attempt to unwind a very large position. A trader holding a very large
position in an otherwise stable market, for example, may find him- or herself in region 4. The risk plane (market/liquidity risk) is of course a simplification of a more complex relationship between markets and position sizes,
involving both exogenous and endogenous components of liquidity risk. In
particular, creating movement along the liquidity axis can be done by moving either across established or emerging markets (i.e., increasing exogenous illiquidity) or within a market by simply increasing one’s position size
(i.e., increasing endogenous illiquidity).
Exogenous illiquidity is the result of market characteristics; it is common to all market players and unaffected by the actions of any one participant (although it can be affected by the joint action of all or almost all
market participants, as happened in several markets in the summer of
1998). The market for liquid securities, such as G-7 currencies, is typically
characterized by heavy trading volumes, stable and small bid-ask
spreads, and stable and high levels of quote depth. Liquidity costs may be
negligible for such positions when marking to market provides a proper
liquidation value. In contrast, markets in emerging currencies or thinly
traded junk bonds are illiquid and are characterized by high volatilities of
spread, quote depth, and trading volume. Endogenous illiquidity, in contrast, is specific to one’s position in the market and varies across market
participants, and the exposure of any one participant is affected by his or
her actions. Endogenous illiquidity is mainly driven by the size of the position: the larger the size, the greater the endogenous illiquidity. A good
way to understand the implications of position size is to consider the
quote depth, which is the relationship between the liquidation price and
the total position size held. Quote depth is defined as the volume of shares
available at the market maker’s quoted price (bid or ask). Market impact
models such as one developed by BARRA quantify this relationship between the transaction price and trade size. If the market order to buy or
sell is smaller than the volume available in the market at the quote, then
the order transacts at the quote. In this case the market impact cost, defined as the cost of immediate execution, will be half of the bid-ask spread.
In our framework, such a position only possesses exogenous liquidity risk
and no endogenous risk. If the size of the order exceeds the quote depth,
the cost of market impact will be higher than the half-spread. The differ-
ence between the total market impact and half-spread is called the incremental market cost, and constitutes the endogenous liquidity component in
our framework. Endogenous liquidity risk can be particularly important
in situations where normally fungible market positions cease to be fungible; a good example would be when the cheapest-to-deliver bond of a futures contract switches. The cheapest-to-deliver bond is a bond that has
the same profile as the bonds used in the futures contract. Once the
cheapest-to-deliver bond changes in profile, for example because duration
is getting shorter because maturity is getting closer, this specific cheapestto-deliver bond is no longer a fungible position. Later, when the bond is
paid back, it disappears from the market. But the futures contract is still in
the market. The bonds in the futures contract have to be “switched” from
time to time to reflect the correct profile in the contract.
Quantitative methods for modeling endogenous liquidity risk have
recently been proposed by Jarrow and Subramanian,38 Chriss and Almgren,39 Bertsimas and Lo,40 and Campbell et al.41 Jarrow and Subramanian,
for example, consider optimal liquidation of an investment portfolio over
a fixed horizon. They characterize the costs and benefits of block sale versus slow liquidation and propose a liquidity adjustment to the standard
VaR measure. The adjustment, however, requires knowledge of the relationship between the trade size and both the quantity discount and the execution lag. Clearly, there is no readily available data source for
quantifying those relationships, which forces one to rely on subjective estimates. In this work we approach the liquidity risk problem from the
other side, focusing on methods for quantifying exogenous rather than endogenous liquidity risk. The purpose is to consider two key facts in the
liquidity discussion. First, fluctuations in exogenous liquidity risk are
often large and important, as is clear from our empirical examples, and
they are relevant for all market players, whether large or small. Second, in
sharp contrast to the situation for endogenous liquidity risk, the data
needed to quantify exogenous liquidity risk is widely available. This is because exogenous liquidity risk is characterized by the volatility of the observed spread with no reference to the relationship of the realized spread
to trade size. The upshot is that we can incorporate liquidity risk into VaR
calculations in a simple and straightforward way.
Traditional VaR measures are obtained from the distribution of portfolio returns computed at the bid-ask average prices. This implies that the
positions can be liquidated at bid-ask prices. This approach conceptually
underestimates risk by neglecting the practical fact that liquidation does
not occur at the bid-ask average price, but rather at the bid-ask average less
half the spread. Thus the spread may fluctuate widely. Use of a simple
measure of exogenous liquidity risk, computed using the distribution of
observed bid-ask spreads, results in much more appropriate risk result,
particularly in emerging market securities. What is the impact for the reg-
Building Blocks for Integration of Risk Categories
ulatory capitalization of a trading operation? BIS regulations stipulate
monitoring of only the number of VaR violations, not of the way that VaR
is computed. Neglecting liquidity risk will lead to underestimation of overall risk, undercapitalization, and too many violations. The BIS regulation,
whether intentionally or not, monitors liquidity risk quite appropriately in
relation to the qualitative aspects of the regulation. Performance evaluation
should also be based on returns adjusted for risk—including liquidity risk.
Some financial institutions do this, and due to higher margins many financial institutions have seen growth in their emerging market trading activity. A risk-adjusted view of performance in those markets should account
not only for market risk but also for liquidity risk. Otherwise, performance
will not be assessed correctly and dealer compensation for liquidity risk
will be distorted as it is not under the control of the dealer.
The integration of the different risk categories depends on the compatibility of approaches, methodologies, and parameters. Credit risk in the form
of specific risks is integrated with market risk in the form of companyspecific spread adjustments on top of the generic treasury yield curves, reflecting the company-specific (credit) risk. As discussed in this chapter,
the integration of credit and market risk models is more challenging. This
is partly due to the fact that the BIS adds values together, ignoring the fact
that the underlying valuation models have different roots, assumptions,
and parameters. The frequency of the credit events (up- or downgrades)
and subsequently the price adjustment follows a different rhythm than
market risk valuation, where daily pricing allows a daily frequency. This
topic is discussed in Secs. 3.6 to 3.8. For some time, VaR was a favorite
measurement approach for everybody and anything. However, more and
more, the practical relevance outweighs the fanciness of valuation. The
different valuation methodologies, including the advantages and the
drawbacks, are discussed to highlight which areas they fit best. Stress testing and limitations of VaR are discussed in detail, emphasizing the important fact that the interpretation of VaR data becomes meaningless unless
the relevance of the valuation models, parameters, and assumptions is reexamined on a regular basis. The relevance includes stability of distributions and volatilities including correlations and time-varying risk.
Liquidity risk is discussed in detail, as it affects market, credit, and operational risks simultaneously. Market prices react with widening spreads,
credit risk reacts with higher specific risks, and operational risk is affected
to exposed transaction settlements.
This chapter presents a critical review of many aspects of the previous chapters. It is important to note that technology has helped to integrate market, credit, and operational risk via higher processing capacities,
networks and shared information, and the increased rapidity with which
companies can close their books and P&L statements. Relevant information for credit risk valuation is disclosed more frequently, which is reflected in more frequent adjustments of credit risk valuations. Systemic
risk is becoming more important. Despite the gap between market and
credit risk categories, unusual market and credit behavior can trigger systemic risk in a significant way given technology and information networks that spread information in real time. One historical example of
systemic risk is the Russian crisis of 1998.
5.11 NOTES
1. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, The New Basel Capital Accord: Consultative Document, Issued for
Comment by 31 May 2001, Basel, Switzerland: Bank for International
Settlement, January 2001.
2. Ibid.
3. The committee will release a complete and fully specified proposal for an
additional round of consultation in early 2002 and will finalize the new
accord during 2003. The Basel Committee envisions an implementation date
of 2005 for the new accord. See Bank for International Settlement (BIS),
Basel Committee on Banking Supervision, “Update on the New Basel
Capital Accord,” press release, Basel, Switzerland: Bank for International
Settlement, June 25, 2001.
4. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate Market Risks,
Basel, Switzerland: Bank for International Settlement, January 1996,
modified September 1997.
5. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, A New Capital Adequacy Framework, Basel, Switzerland: Bank
for International Settlement, June 1999.
6. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, “Progress Towards Completion of the New Basel Capital
Accord,” press release, Basel, Switzerland: Bank for International
Settlement, December 13, 2001.
7. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, “Quantitative Impact Survey of New Basel Capital Accord,”
press release, Basel, Switzerland: Bank for International Settlement, October
1, 2002.
8. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, “Update on the New Basel Capital Accord,” press release,
Basel, Switzerland: Bank for International Settlement, June 25, 2001;
“Update on the New Basel Capital Accord, Issue 2,” press release, Basel,
Switzerland: Bank for International Settlement, September 21, 2001; Results
of the Second Quantitative Impact Study, Basel, Switzerland: Bank for
Building Blocks for Integration of Risk Categories
International Settlement, November 5, 2001; Potential Modifications to the
Committee’s Proposals, Basel, Switzerland: Bank for International Settlement,
November 5, 2001; The Quantitative Impact Study for Operational Risk:
Overview of Individual Loss Data and Lessons Learned, Basel, Switzerland: Bank
for International Settlement, January 2002.
9. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Results of the Second Quantitative Impact Study, Basel,
Switzerland: Bank for International Settlement, November 5, 2001.
10. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, The Quantitative Impact Study for Operational Risk: Overview of
Individual Loss Data and Lessons Learned, Basel, Switzerland: Bank for
International Settlement, January 2002.
11. Ibid.
12. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, The New Basel Capital Accord: Consultative Document, Issued for
Comment by 31 May 2001, Basel, Switzerland: Bank for International
Settlement, January 2001, para. 19ff.
13. Ibid., para. 586 ff.
14. Ibid., para. 633 ff.
15. The latest approved version, dated May 20, 2001, is officially titled “AIMRPPS Standards, the U.S. and Canadian Version of GIPS.” For details, see and
16. See Anil Bangia, Francis X. Diebold, Til Schuermann, and John D.
Stroughair, Modeling Liquidity Risk, with Implications for Traditional Market
Risk Measurement and Management, University of Pennsylvania, Financial
Institutions Center, The Wharton School, June, 1999.
17. See for instance E. I. Altman and D. L. Kao, “Examining and Modeling
Corporate Bond Rating Drift,” working paper, New York University
Salomon Center, New York, 1991. These researchers find that there is
positive autocorrelation in S&P downgrades, so a downgrade implies a
higher likelihood of a downgrade in the following period. Looking at the
S&P rating data, the study finds that an upgrade tends to lead to a “quiet”
period. However, this finding applies in particular to the S&P rating
methodology. Other credit rating systems are not necessarily subject to this
problem in the same way given different assumptions and approaches.
18. Bank for International Settlement (BIS), Basel Committee on Banking
Supervision, Amendment to the Capital Accord to Incorporate